Nonlinear Potential Theory

Our research group is mainly interested in analysis on metric spaces, and in particular nonlinear potential theory associated with p-harmonic functions and quasiminimizers in Euclidean and metric spaces. We are also interested in first-order Sobolev spaces, in particular the so-called Newtonian spaces on metric spaces.

Here are links to newer versions of this page in English and Swedish.

Conferences

We have organized the following conferences in Linköping:

Geometric Analysis on Metric Spaces, 22-24 May 2017
PDEs, Potential Theory and Function Spaces, 14-18 June 2015
Nonlinear problems for Δp and Δ, 10-14 August 2009

Members of the group

Anders Björn (Orcid 0000-0002-9677-8321)
Jana Björn (Orcid 0000-0002-1238-6751)
Andreas Christensen
Daniel Hansevi (Orcid 0000-0002-2902-3279)
Ismail Mirumbe, web page at the Makerere University
Abubakar Mwasa
Tomas Sjödin (Orcid 0000-0002-2962-5755)

Former members of the group

Tomasz Adamowicz
Daniel Carlsson
Zohra Farnana
Rebekah Jones
Panu Lahti (Orcid 0000-0002-1058-1625)
Lukáš Malý (Orcid 0000-0003-2083-9180)
Nageswari Shanmugalingam (Orcid 0000-0002-2891-5064)

Collaboration

People with whom we collaborate or have close contacts with include the following people.

Hiroaki Aikawa Hokkaido University, Sapporo
Stephen Gardiner at University College Dublin
Ugo Gianazza at University of Pavia
Agnieszka Kałamajska at Warsaw University
Juha Kinnunen and Riikka Korte at Aalto University, Helsinki
Visa Latvala at University of Eastern Finland, Joensuu
Juha Lehrbäck and Mikko Parviainen at Jyväskylä University
Xining Li at Sun Yat-sen University, Guangzhou (Canton)
Jan Malý at Charles University, Prague
Olli Martio and Xiao Zhong at Helsinki University
Juhana Siljander at University of Chicago

Publications

The list below contains the mathematical publications (in reverse chronological order) of the members of the group.

Books

A. Björn and J. Björn, Nonlinear Potential Theory on Metric Spaces, EMS Tracts in Mathematics 17, European Mathematical Society, Zürich, 2011, 415 pp, ISBN 978-3-03719-099-9. Distributed by EMS and AMS. Corrections and clarifications (last updated 3 May 2018).
The authors' profit from this book is donated to Barndiabetesfonden (The Swedish Child Diabetes Fund).
A. Asratian, A. Björn and B. O. Turesson, Diskret Matematik, 15th ed., Matematiska institutionen, Linköpings universitet, 2015, 285 pp. (Swedish).

Ph.D. theses

L. Malý, Sobolev-Type Spaces: Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 1591, Linköping, 2014, 168 pp (supervisors Anders Björn, Jana Björn, Tomas Sjödin).
It consists of the following four papers (the links here are to slightly different arXiv versions):
Newtonian spaces based on quasi-Banach function lattices (this paper will appear in Math. Scand.),
Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices (this paper has appeared in Ann. Acad. Sci. Fenn. Math. 38 (2013), 727-745),
Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators,
Fine properties of Newtonian functions and the Sobolev capacity on metric measure spaces.
Z. Farnana, The Double Obstacle Problem on Metric Spaces, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 1283, Linköping, 2009, 94 pp (supervisors Jana Björn, Anders Björn, Lars-Erik Andersson).
T. Sjödin, Topics in Potential Theory: Quadrature Domains, Balayage and Harmonic Measure, Doctoral Thesis in Mathematics, TRITA-MAT-05-MA-05, Royal Institute of Technology, Stockholm, 2005, 232 pp (supervisor Björn Gustafsson).
J. Björn, Interior Regularity and Boundary Behaviour of Solutions to Second Order Elliptic Equations, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 446, Linköping, 1996, 92 pp (supervisor Vladimir Maz'ya).
A. Björn, Removable Singularities for Hardy Spaces of Analytic Functions, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 365, Linköping, 1994, 74 pp (supervisor Lars Inge Hedberg).

Licentiate theses

L. Malý, Newtonian Spaces Based on Quasi-Banach Function Lattices, Licentiate thesis, Linköping Studies in Science and Technology. Theses. No. 1543, Linköping, 2012, 60 pp. ArXiv versions of the two papers are available here Newtonian spaces based on quasi-Banach function lattices and Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices (supervisors Anders Björn, Jana Björn, Tomas Sjödin).
Z. Farnana, The Double Obstacle Problem on Metric Spaces, Licentiate thesis, Linköping Studies in Science and Technology. Theses. No. 1342, Linköping, 2008, 52 pp (supervisors Jana Björn, Anders Björn, Lars-Erik Andersson).

For Master's and Bachelor's theses see the bottom of this page.

Preprints

A. Björn and J. Björn, A uniqueness result for functions with zero fine gradient on quasiconnected sets, Preprint, 2018. arXiv
A. Björn, J. Björn and X. Li, Sphericalization and p-harmonic functions on unbounded domains in Ahlfors regular metric spaces, Preprint, 2018. arXiv
A. Björn, J. Björn and M. Parviainen, The tusk condition and Petrovskii criterion for the normalized p-parabolic equation, Preprint, 2017. arXiv
A. Björn, J. Björn and N. Shanmugalingam, Locally p-admissible measures on R, Preprint, 2018. arXiv
A. Björn, J. Björn and N. Shanmugalingam, The Liouville theorem for p-harmonic functions and quasiminimizers with finite energy Preprint, 2018. arXiv
P. Lahti, L. Malý, N. Shanmugalingam and G. Speight, Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient, Preprint, 2017. arXiv, Preprint CVGMT
L. Malý, Trace and extension theorems for Sobolev-type functions in metric spaces, Preprint, 2017. arXiv

Refereed articles

To appear
A. Björn, The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications, to appear in Complex Var. Elliptic Equ. doi:10.1080/17476933.2017.1410799 Journal, arXiv
A. Björn and J. Björn, Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces, to appear in J. Differential Equations. doi:10.1016/j.jde.2018.07.029 Journal, arXiv
S. J. Gardiner, M. Ghergu and T. Sjödin, Isoperimetric inequalities for Bergman analytic content, to appear in Indiana Univ. Math. J. Preprint
S. J. Gardiner and T. Sjödin, On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions, to appear in Math. Bohem.


2018
H. Aikawa, A. Björn, J. Björn and N. Shanmugalingam, Dichotomy of global capacity density in metric measure spaces, Adv. Calc. Var. 11 (2018), 387-404. doi:10.1515/acv-2016-0066 Journal, arXiv, Preprint CVGMT
A. Björn and J. Björn, Local and semilocal Poincaré inequalities on metric spaces, J. Math. Pures Appl. 119 (2018), 158-192. doi:10.1016/j.matpur.2018.05.005 Journal, arXiv (Share link valid until 5 Dec 2018.)
A. Björn and J. Björn, Tensor products and sums of p-harmonic functions, quasiminimizers and p-admissible weights, Proc. Amer. Math. Soc. 146 (2018), 5195-5203. doi:10.1090/proc/14170 Journal, arXiv
A. Björn, J. Björn, U. Gianazza and J. Siljander, Boundary regularity for the porous medium equation, Arch. Ration. Mech. Anal. 230 (2018), 493-538. doi:10.1007/s00205-018-1251-3 Journal (Open choice), arXiv
A. Björn, J. Björn and V. Latvala, The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces, J. Anal. Math. 135 (2018), 59-83. doi:10.1007/s11854-018-0029-8 Journal (Open choice), Preprint Institut Mittag-Leffler no. 41 (40), 2014. arXiv
A. Björn, J. Björn and T. Sjödin, The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications, Rev. Mat. Iberoam. 34 (2018), 1323-1360. doi:10.4171/RMI/1025 Journal, arXiv
S. J. Gardiner, M. Ghergu and T. Sjödin, Analytic content and the isoperimetric inequality in higher dimensions, J. Funct. Anal. 275 (2018), 2284-2298. Journal, arXiv
D. Hansevi, The Perron method for p-harmonic functions in unbounded sets in Rn and metric spaces, Math. Z. 288 (2018), 55-74. doi:10.1007/s00209-017-1877-0 Journal (Open choice), arXiv
P. Lahti, L. Malý and N. Shanmugalingam, An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability, Anal. Geom. Metr. Spaces 6 (2018), 1-31. doi:10.1515/agms-2018-0001 Journal, arXiv
L. Malý, Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators, J. Anal. Math. 134 (2018), 1-54. doi:10.1007/s11854-018-0001-7 Journal, arXiv
L. Malý and N. Shanmugalingam, Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity, J. Differential Equations 265 (2018), 2431-2460. doi:10.1016/j.jde.2018.04.038 Journal, arXiv, Preprint CVGMT
L. Malý, N. Shanmugalingam and M. Snipes, Trace and extension theorems for functions of bounded variation, Ann. Sc. Norm. Super. Pisa Cl. Sci. 18 (2018), 313-341. Journal, arXiv


2017
A. Björn, J. Björn and U. Gianazza, The Petrovskii criterion and barriers for degenerate and singular p-parabolic equations, Math. Ann. 368 (2017), 885-904. doi:10.1007/s00208-016-1415-0 Journal, arXiv
A. Björn, J. Björn, J. T. Gill and N. Shanmugalingam, Geometric analysis on Cantor sets and trees, J. Reine Angew. Math. 725 (2017), 63-114. doi:10.1515/crelle-2014-0099 Journal, arXiv
A. Björn, J. Björn and R. Korte, Minima of quasisuperminimizers, Nonlinear Anal. 155 (2017), 264-284. doi:10.1016/j.na.2017.02.003 Journal, arXiv
A. Björn, J. Björn and J. Lehrbäck, Sharp capacity estimates for annuli in weighted Rn and in metric spaces, Math. Z. 286 (2017), 1173-1215. doi:10.1007/s00209-016-1797-4 Journal (Open choice), Preprint Institut Mittag-Leffler no. 17 (6), 2013. arXiv
A. Björn, J. Björn and J. Lehrbäck, The annular decay property and capacity estimates for thin annuli, Collect. Math. 68 (2017), 229-241. doi:10.1007/s13348-016-0178-y Journal, arXiv
A. Björn, J. Björn and J. Malý, Quasiopen and p-path open sets, and characterizations of quasicontinuity, Potential Anal. 46 (2017), 181-199. doi:10.1007/s11118-016-9580-z Journal (Open choice), arXiv


2016
J. Arnlind, A. Björn and J. Björn, An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces, Nonlinear Anal. 134 (2016), 70-104. doi:10.1016/j.na.2015.12.010 Journal, arXiv
A. Björn, J. Björn and V. Latvala, Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets, Ann. Acad. Sci. Fenn. Math. 41 (2016), 551-560. doi:10.5186/aasfm.2016.4130 pdf, Journal, arXiv
A. Björn, J. Björn and N. Shanmugalingam, The Mazurkiewicz distance and sets that are finitely connected at the boundary, J. Geom. Anal. 26 (2016), 873-897. doi:10.1007/s12220-015-9575-9 Journal, Preprint Institut Mittag-Leffler no. 14 (10), 2013. arXiv
J. Björn, Sharp exponents and a Wiener type condition for boundary regularity of quasiminimizers, Adv. Math. 301 (2016), 804-819. doi:10.1016/j.aim.2016.06.024 Journal, arXiv.
L. Malý, Newtonian spaces based on quasi-Banach function lattices, Math. Scand. 119 (2016), 133-160. doi:10.7146/math.scand.a-24188 Journal, arXiv
L. Malý, Fine properties of Newtonian functions and the Sobolev capacity on metric measure spaces, Rev. Mat. Iberoam. 32 (2016), 219-255. doi:10.4171/RMI/884 Journal, arXiv
T. Sjödin, A new approach to Sobolev spaces in metric measure spaces, Nonlinear Anal. 142 (2016), 194-237. doi:10.1016/j.na.2016.04.010 Journal, arXiv


2015
T. Adamowicz, The geometry of planar p-harmonic mappings: convexity, level curves and the isoperimetric inequality, Ann. Sc. Norm. Super. Pisa Cl. Sci. 14 (2015), 263-292. doi:10.2422/2036-2145.201201_010 Journal, Preprint
T. Adamowicz, P. Harjulehto and P. Hästö, Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces, Math. Scand. 116 (2015), 5-22. doi:10.7146/math.scand.a-20448 Journal, Preprint
A. Björn, The Dirichlet problem for p-harmonic functions on the topologist's comb, Math. Z. 279 (2015), 389-405. doi:10.1007/s00209-014-1373-8 Journal, arXiv
A. Björn and J. Björn, Obstacle and Dirichlet problems on arbitrary nonopen sets, and fine topology, Rev. Mat. Iberoam. 31 (2015), 161-214. doi:10.4171/RMI/830 Journal, arXiv
A. Björn, J. Björn, U. Gianazza and M. Parviainen, Boundary regularity for degenerate and singular parabolic equations, Calc. Var. Partial Differential Equations 52 (2015), 797-827. doi:10.1007/s00526-014-0734-9 Journal, Preprint Institut Mittag-Leffler no. 4 (20), 2013, arXiv
A. Björn, J. Björn and V. Latvala, The weak Cartan property for the p-fine topology on metric spaces, Indiana Univ. Math. J. 64 (2015), 915-941. doi:10.1512/iumj.2015.64.5527 Journal, Preprint Institut Mittag-Leffler no. 5 (18), 2013. arXiv
A. Björn, J. Björn and N. Shanmugalingam, The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities, J. Differential Equations 259 (2015), 3078-3114. doi:10.1016/j.jde.2015.04.014 Journal, arXiv
D. Hansevi, The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rn and metric spaces, Ann. Acad. Sci. Fenn. Math. 40 (2015), 89-108. doi:10.5186/aasfm.2015.4005 pdf, Journal, arXiv


2014
T. Adamowicz, Phragmen-Lindelöf theorems for equations with nonstandard growth, Nonlinear Anal. 97 (2014), 169-184. doi:10.1016/j.na.2013.11.018 Journal, Preprint
T. Adamowicz, A. Björn and J. Björn, Regularity of p(·)-superharmonic functions, the Kellogg property and semiregular boundary points, Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), 1131-1153. doi:10.1016/j.anihpc.2013.07.012 Journal, arXiv
A. Björn and J. Björn, The variational capacity with respect to nonopen sets in metric spaces, Potential Anal. 40 (2014), 57-80. doi:10.1007/s11118-013-9341-1 Journal, arXiv
S.J. Gardiner and T. Sjödin, Stationary boundary points for a Laplacian growth problem in higher dimensions, Arch. Ration. Mech. Anal. 213 (2014), 503-526. doi:10.1007/s00205-014-0750-0 Journal


2013
T. Adamowicz, A. Björn, J. Björn and N. Shanmugalingam, Prime ends for domains in metric spaces, Adv. Math. 238 (2013), 459-505. doi:10.1016/j.aim.2013.01.014 Journal, arXiv
L. Malý, Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices, Ann. Acad. Sci. Fenn. Math. 38 (2013), 727-745. doi:10.5186/aasfm.2013.3831 pdf, Journal, arXiv
H. Shahgholian and T. Sjödin, Harmonic balls and the two-phase Schwarz function, Complex Var. Elliptic Equ. 58 (2013), 837-852. doi:10.1080/17476933.2011.622046 Journal, arXiv


2012
L. Malý, Calderón-type theorems for operators with non-standard endpoint behavior on Lorentz spaces, Math. Nachr. 285 (2012), 1450-1465. doi:10.1002/mana.201100095 Journal
S.J. Gardiner and T. Sjödin, Two-phase quadrature domains, J. Anal. Math. 116 (2012), 335-354. doi:10.1007/s11854-012-0009-3 Journal


2011
A. Björn and H. Riesel Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), 1865-1866. doi:10.1090/S0025-5718-10-02371-9 Journal
A. Björn and J. Björn, Power-type quasiminimizers, Ann. Acad. Sci. Fenn. Math. 36 (2011), 301-319. doi:10.5186/aasfm.2011.3619 pdf, Journal
Z. Farnana, Pointwise regularity for solutions of double obstacle problems on metric spaces, Math. Scand. 109 (2011), 185-200. doi:10.7146/math.scand.a-15184 Journal


2010
A. Björn, p-harmonic functions with boundary data having jump discontinuities and Baernstein's problem, J. Differential Equations 249 (2010), 1-36. doi:10.1016/j.jde.2010.03.002 Journal
A. Björn, Cluster sets for Sobolev functions and quasiminimizers, J. Anal. Math. 112 (2010), 49-77. doi:10.1007/s11854-010-0025-0 Journal
A. Björn, J. Björn and N. Marola, BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 1489-1505. doi:10.1016/j.anihpc.2010.09.005 Journal
A. Björn, J. Björn and M. Parviainen, Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces, Rev. Mat. Iberoam. 26 (2010), 147-174. doi:10.4171/RMI/598 Journal
J. Björn, Orlicz-Poincaré inequalities, maximal functions and AΦ-conditions, Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), 31-48. doi:10.1017/S0308210508000772 Journal
M. Eleuteri, Z. Farnana, O. E. Kansanen and R. Korte, Stability of solutions of the double obstacle problem on metric spaces, J. Anal. 18 (2010), 145-160. Journal
Z. Farnana, Continuous dependence on obstacles for the double obstacle problem on metric spaces, Nonlinear Anal. 73 (2010), 2819-2830. doi:10.1016/j.na.2010.06.023 Journal
Z. Farnana, Convergence results for obstacle problems on metric spaces, J. Math. Anal. Appl. 371 (2010), 436-446. doi:10.1016/j.jmaa.2010.05.044 Journal


2009
A. Björn, J. Björn, T. Mäkäläinen and M. Parviainen, Nonlinear balayage on metric spaces, Nonlinear Anal. 71 (2009), 2153-2171. doi:10.1016/j.na.2009.01.051 Journal, Parallel publication
A. Björn and O. Martio, Pasting lemmas and characterizations of boundary regularity for quasiminimizers, Results Math. 55 (2009), 265-279. doi:10.1007/s00025-009-0437-2 Journal
J. Björn, Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations, Calc. Var. Partial Differential Equations 35 (2009), 481-496. doi:10.1007/s00526-008-0216-z Journal
Z. Farnana, The double obstacle problem on metric spaces, Ann. Acad. Sci. Fenn. Math. 34 (2009), 261-277. Journal


2008
A. Björn, A regularity classification of boundary points for p-harmonic functions and quasiminimizers, J. Math. Anal. Appl. 338 (2008), 39-47. doi:10.1016/j.jmaa.2007.04.068 Journal, Parallel publication
A. Björn, J. Björn and N. Shanmugalingam, Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions on metric spaces, Houston J. Math. 34 (2008), 1197-1211. Journal
J. Björn, Fine continuity on metric spaces, Manuscripta Math. 125 (2008), 369-381. doi:10.1007/s00229-007-0154-7 Journal
S. J. Gardiner and T. Sjödin, Convexity and the exterior inverse problem of potential theory, Proc. Amer. Math. Soc. 136 (2008), 1699-1703. doi:10.1090/S0002-9939-07-09228-3 Journal


2007
A. Björn, Weak barriers in nonlinear potential theory, Potential Anal. 27 (2007), 381-387. doi:10.1007/s11118-007-9064-2 Journal, Parallel publication
A. Björn and J. Björn, Approximations by regular sets and Wiener solutions in metric spaces, Comment. Math. Univ. Carolin. 48 (2007), 343-355. pdf, Journal
A. Björn, J. Björn and N. Shanmugalingam Sobolev extensions of Hölder continuous and characteristic functions on metric spaces, Canadian J. Math. 59 (2007), 1135-1153. doi:10.4153/CJM-2007-049-7 Journal
J. Björn and N. Shanmugalingam, Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces, J. Math. Anal. Appl. 332 (2007), 190-208. doi:10.1016/j.jmaa.2006.09.064 Journal
S. J. Gardiner and T. Sjödin, Quadrature domains for harmonic functions, Bull. Lond. Math. Soc. 39 (2007), 586-590. doi:10.1112/blms/bdm047 Journal
T. Sjödin, On the structure of partial balayage, Nonlinear Anal. 67 (2007), 94-102. doi:10.1016/j.na.2006.05.001 Journal
T. Sjödin, Approximation in the cone of positive harmonic functions, Potential Anal. 27 (2007), 271-280. doi:10.1007/s11118-007-9059-z Journal


2006
A. Björn, Removable singularities for bounded p-harmonic and quasi(super)harmonic functions, Ann. Acad. Sci. Fenn. Math. 31 (2006), 71-95. Journal
A. Björn, Removable singularities in weighted Bergman spaces, Czechoslovak Math. J. 56 (2006), 179-227. doi:10.1007/s10587-006-0012-x Journal, Parallel publication
A. Björn, A weak Kellogg property for quasiminimizers, Comment. Math. Helv. 81 (2006), 809-825. doi:10.4171/CMH/75 Journal
A. Björn and J. Björn, Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces, J. Math. Soc. Japan 58 (2006), 1211-1232. Journal
A. Björn, J. Björn and N. Shanmugalingam, A problem of Baernstein on the equality of the p-harmonic measure of a set and its closure, Proc. Amer. Math. Soc. 134 (2006), 509-519. doi:10.1090/S0002-9939-05-08187-6 Journal, Parallel publication
A. Björn and N. Marola, Moser iteration for (quasi)minimizers on metric spaces, Manuscripta Math. 121 (2006), 339-366. doi:10.1007/s00229-006-0040-8 Journal, Parallel publication
J. Björn, S. Buckley and S. Keith, Admissible measures in one dimension, Proc. Amer. Math. Soc. 134 (2006), 703-705. doi:10.1090/S0002-9939-05-07925-6 Journal
T. Sjödin, Mother bodies of algebraic domains in the complex plane, Complex Var. Elliptic Equ. 51 (2006), 357-369. doi:10.1080/17476930600610049 Journal


2005
A. Björn, Characterizations of p-superharmonic functions on metric spaces, Studia Math. 169 (2005), 45-62. doi:10.4064/sm169-1-3 Journal
A. Björn and H. Riesel, Table errata on "Factors of generalized Fermat numbers", Math. Comp. 74 (2005), 2099. doi:10.1090/S0025-5718-05-01816-8 Journal
J. Björn and J. Onninen, Orlicz capacities and Hausdorff measures on metric spaces, Math. Z. 251 (2005), 131-146. doi:10.1007/s00209-005-0792-y Journal


2003
A. Björn, Removable singularities for analytic functions in BMO and locally Lipschitz spaces, Math. Z. 244 (2003), 805-835. doi:10.1007/s00209-003-0524-0 Journal, Parallel publication
A. Björn, J. Björn and N. Shanmugalingam, The Dirichlet problem for p-harmonic functions on metric spaces, J. Reine Angew. Math. 556 (2003), 173-203. doi:10.1515/crll.2003.020 Journal
A. Björn, J. Björn and N. Shanmugalingam, The Perron method for p-harmonic functions, J. Differential Equations 195 (2003), 398-429. doi:10.1016/S0022-0396(03)00188-8 Journal, Parallel publication


2002
N. Arcozzi and A. Björn, Dominating sets for analytic and harmonic functions and completeness of weighted Bergman spaces, Math. Proc. Roy. Irish Acad. 102A (2002), 175-192. doi:10.3318/PRIA.2002.102.2.175 Journal
A. Björn, Properties of removable singularities for Hardy spaces of analytic functions, J. Lond. Math. Soc. 66 (2002), 651-670. doi:10.1112/S002461070200354X Journal
J. Björn, Boundary continuity for quasiminimizers on metric spaces, Illinois J. Math. 46 (2002), 383-403. Journal
J. Björn, Mappings with dilatation in Orlicz spaces, Collect. Math. 53 (2002), 303-311.


2001
A. Björn, Removable singularities for H p spaces of analytic functions, 0<p<1, Ann. Acad. Sci. Fenn. Math. 26 (2001), 155-174. Journal
J. Björn, Boundedness and differentiability for nonlinear elliptic systems, Trans. Amer. Math. Soc. 353 (2001), 4545-4565. doi:10.1090/S0002-9947-01-02834-3 Journal
J. Björn, Poincar\'e inequalities for powers and products of admissible weights, Ann. Acad. Sci. Fenn. Math. 26 (2001), 175-188. Journal
J. Björn, P. MacManus and N. Shanmugalingam, Fat sets and pointwise boundary estimates for p-harmonic functions in metric spaces, J. Anal. Math. 85 (2001), 339-369. doi:10.1007/BF02788087 Journal


2000
J. Björn, Lq-differentials for weighted Sobolev spaces, Michigan Math. J. 47 (2000), 151-161. doi:10.1307/mmj/1030374674 Journal
J. Björn and V. Maz'ya, Capacitary estimates for solutions of the Dirichlet problem for second order elliptic equations in divergence form, Potential Anal. 12 (2000), 81-113. doi:10.1023/A:1008670611142 Journal


1998
A. Björn Removable singularities for Hardy spaces, Complex Variables Theory Appl. 35 (1998), 1-25. doi:10.1080/17476939808815069 Journal, Parallel publication
A. Björn, Removable singularities on rectifiable curves for Hardy spaces of analytic functions. Math. Scand. 83 (1998), 87-102. doi:10.7146/math.scand.a-13844 Journal
A. Björn and Riesel, H., Factors of generalized Fermat numbers, Math. Comp. 67 (1998), 441-446 + 49 pp. of tables on micro-fiche. doi:10.1090/S0025-5718-98-00891-6 Journal


1997
J. Björn, Regularity at infinity for a mixed problem for degenerate elliptic operators in a half-cylinder, Math. Scand. 81 (1997), 101-126. pdf, Journal


1994
J. Ježková [Björn], Boundedness and pointwise differentiability of weak solutions to quasi-linear elliptic differential equations and variational inequalities, Comment. Math. Univ. Carolin. 35 (1994), 63-80. pdf, Journal

Refereed conference proceedings

2014
S. J. Gardiner and T. Sjödin, Quadrature domains and their two-phase counterparts, in Harmonic and Complex Analysis and its Applications, pp. 261-285, Trends Math., Birkhäuser, Cham, 2014. doi:10.1007/978-3-319-01806-5_5 Publication


2009
A. Björn and J. Björn, First-order Sobolev spaces on metric spaces, in Function Spaces, Inequalities and Interpolation (Paseky, 2009), pp. 1-29, Matfyzpress, Prague, 2009.
S. J. Gardiner and T. Sjödin, Partial balayage and the exterior inverse problem of potential theory, in Potential theory and stochastics in Albac, Theta Ser. Adv. Math. 11, pp. 111-123, Theta, Bucharest, 2009.
S. J. Gardiner and T. Sjödin, Potential theory in Denjoy domains, in Analysis and mathematical physics, pp. 143-166, Trends Math., Birkhäuser, Basel, 2009. doi:10.1007/978-3-7643-9906-1_8 Publication


2006
J. Björn, Wiener criterion for Cheeger p-harmonic functions on metric spaces, in Potential Theory in Matsue, Advanced Studies in Pure Mathematics 44, pp. 103-115, Mathematical Society of Japan, Tokyo, 2006. pdf, Publication


2005
T. Sjödin, Quadrature identities and deformation of quadrature domains, in Quadrature Domains and their Applications, Operator Theory, Advances and Applications 156, pp. 239-255, Birkhäuser, Basel, 2005. doi:10.1007/3-7643-7316-4_12 Publication


2003
A. Björn, p-harmonic measures and the Perron method for p-harmonic functions}, in Future Trends in Geometric Function Theory RNC Workshop Jyväskylä 2003, Rep. Univ. Jyväskylä Dep. Math. Stat. 92, pp. 23-29, Univ. Jyväskylä, Jyväskylä, 2003.
A. Björn, Removable singularities for analytic functions in Hardy spaces, BMO and locally Lipschitz spaces, in Progress in Analysis. Proceedings of the 3rd International ISAAC Congress (Berlin, 2001), vol. 1, pp. 445-450, World Scientific, Singapore, 2003. doi:10.1142/9789812794253_0050 Publication
J. Björn, Dirichlet problem for p-harmonic functions in metric spaces, in Future Trends in Geometric Function Theory RNC Workshop Jyväskylä 2003, Rep. Univ. Jyväskylä Dep. Math. Stat. 92, pp. 31-38, Univ. Jyväskylä, Jyväskylä, 2003.


1996
A. Björn, Removable singularities for Hardy spaces in subdomains of C, in Potential Theory - ICPT 94 (J. Král, J. Lukes, I. Netuka and J. and Veselý, eds.), pp. 287-295, de Gruyter, Berlin-New York, 1996. doi:10.1515/9783110818574.287 Publication
A. Björn, Some open problems relating removable singularities for Hardy spaces and Hausdorff measures, in Potential Theory - ICPT 94 (J. Král, J. Lukes, I. Netuka and J. and Veselý, eds.), p. 474, de Gruyter, Berlin-New York, 1996. doi:10.1515/9783110818574.473 Publication


1993
H. Riesel and A. Björn, Generalized Fermat numbers, in Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics (W.Gautschi, ed.), Proc. Symp. Appl. Math. 48, pp. 583-587, Amer. Math. Soc., Providence, RI, 1994. doi:10.1090/psapm/048/1314895 Publication

Popular science articles

2016
A. Björn, HbA1c according to different standards, 2016. Publication
A. Björn, HbA1c enligt olika standarder, 2016 (in Swedish). Publication
A. Björn, HbA1c podle různých standardů, 2016 (in Czech). Publication


2004
A. Björn, Why is there no Nobel prize in mathematics?, De Morgan Association Newsletter, Issue 11, Dept. of Maths., University College London, London, 2003/04.

Master's thesis

Andreas Christensen, Capacity estimates and Poincaré inequalities for the weighted bow-tie, 2017 (supervisor A. Björn, examiner J. Björn).
Hanna Svensson [Ström], Radiella vikter i Rn och lokala dimensioner, 2014 (supervisor J. Björn, examiner A. Björn).
Hannes Uppman, The Reflection Principle for One-dimensional Quasiminimizers, 2009 (supervisor A. Björn).
Karl Tomas Andersson [Lööw], An iterative solution method for p-harmonic functions on finite graphs with an implementation, 2009 (supervisor A. Björn). Thesis, Program
John Karlsson, Lebesgue points, Hölder continuity and Sobolev functions, 2008 (supervisor J. Björn).
Patrik Leifson, Fractal sets and dimensions, 2006 (supervisor J. Björn).
David Färm, Upper gradients and Sobolev spaces on metric spaces, 2006 (supervisor J. Björn).
Lisa Hallingström, Primkontroll av tal på formen k · 2q+1 med program i Fortran 77, 2003 (supervisor A. Björn).
Svante Landgraf, Dominating sets for real parts of holomorphic functions, 2003 (supervisor A. Björn).
Joakim Gustafsson, An implementation and optimization of an algorithm for reducing formulae in second-order logic, 1996 (supervisor P. Doherty, examiner A. Björn).

Bachelor's thesis

Maria Miranda Navarro, Comparative Study of Several Bases in Functional Analysis, 2018 (supervisor J. Björn).
Erik Jönsson, Tug-of-war games of the p-Laplacian for analysts, 2018 (supervisor J. Björn, examiner A. Björn).
Erik Sätterqvist, Sequences of functions: Different notions of convergence and how they are reelated, 2018 (supervisor J. Björn, examiner A. Björn).
Sofia Svensson, Lokala dimensioner och radiella vikter i Rn, 2017 (supervisor J. Björn, examiner A. Björn).
Karl Nygren, Trust logics and their horn fragments: formalizing socio-cognitive aspects of trust, 2015 (superviser Andrzej Szałas, examiner A. Björn).
Hannah Schäfer Sjöberg, A problem in number theory, 2013 (supervisor A. Björn).
Adam Schill Collberg, The last two digits of mk, 2012 (supervisor Gao Peng, examiner A. Björn).
Jimmie Enhäll, Ett problem inom talteori, 2005 (supervisor A. Björn).
Tobias Svensson, Common factors in generalized Fermat numbers, 2005 (supervisor A. Björn).


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Last updated: 2018-10-19