# Nonlinear Potential Theory

Our research group is mainly interested in 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 is a description of some of our research in English and Swedish.

## We are organizing the workshop Geometric Analysis on Metric Spaces, 22--24 May 2017 in Linköping

We have organized the conferences: PDEs, Potential Theory and Function Spaces 14-18 June 2015 in Linköping, and Nonlinear problems for $\Delta_p$ and $\Delta$ , 10-14 August 2009 in Linköping.

## Members of the group

Anders Björn (Orcid 0000-0002-9677-8321)
Jana Björn (Orcid 0000-0002-1238-6751)
Daniel Hansevi (Orcid 0000-0002-2902-3279)
Panu Lahti
Abubakar Mwasa
Nageswari Shanmugalingam (Orcid 0000-0002-2891-5064)
Tomas Sjödin (Orcid 0000-0002-2962-5755)

#### Former members of the group

Daniel Carlsson
Rebekah Jones
Lukáš Malý (Orcid 0000-0003-2083-9180)
Zohra Farnana

## 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
Jim Gill at Saint Louis University
Agnieszka Kałamajska at Warsaw University
Juha Kinnunen and Riikka Korte at Aalto University, Helsinki
Visa Latvala at University of Eastern Finland, Joensuu
Juha Lehrbäck, Mikko Parviainen and Juhana Siljander at Jyväskylä University
Olli Martio and Xiao Zhong at Helsinki University
Jan Malý at Charles University, Prague
Stephen Buckley at University of Maynooth

## 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 2 May 2017).
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).

### Preprints

A. Björn, The Kellogg property for p-harmonic functions with respect to the Mazurkiewicz boundary, Preprint, 2017. arXiv
A. Björn and J. Björn, Local and semilocal Poincaré inequalities on metric spaces, Preprint, 2017. arXiv
A. Björn and J. Björn, Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces, Preprint, 2017. arXiv
A. Björn and J. Björn, Tensor products and sums of p-harmonic functions, quasiminimizers and p-admissible weights, Preprint, 2017. arXiv
S. J. Gardiner, M. Ghergu and T. Sjödin, Analytic content and the isoperimetric inequality in higher dimensions, Preprint, 2017. 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,
L. Malý and N. Shanmugalingam, Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity, Preprint, 2016. arXiv, Preprint CVGMT

### Refereed articles

To appear
H. Aikawa, A. Björn, J. Björn and N. Shanmugalingam, Dichotomy of global capacity density in metric measure spaces, to appear in Adv. Calc. Var. doi:10.1515/acv-2016-0066 Journal, arXiv, Preprint CVGMT
A. Björn, J. Björn and U. Gianazza, The Petrovskii criterion and barriers for degenerate and singular p-parabolic equations, to appear in Math. Ann. doi:10.1007/s00208-016-1415-0 Journal, arXiv
A. Björn, J. Björn and V. Latvala, The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces, to appear in J. Anal. Math., 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, to appear in Rev. Mat. Iberoam. arXiv
D. Hansevi, The Perron method for p-harmonic functions in unbounded sets in Rn and metric spaces, to appear in Math. Z. doi:10.1007/s00209-017-1877-0 Journal (Open choice), arXiv
L. Malý, Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators, to appear in J. Anal. Math. arXiv
L. Malý, N. Shanmugalingam and M. Snipes, Trace and extension theorems for functions of bounded variation, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. arXiv

2017
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 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. 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. 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. 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. 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. Journal, arXiv

2014
T. Adamowicz, Phragmen-Lindelöf theorems for equations with nonstandard growth, Nonlinear Anal. 97 (2014), 169-184. Journal, Preprint
T. Adamowicz, A. Björn and J. Björn, Regularity of $p(\cdot)$-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. 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. Journal, arXiv
H. Shahgholian and T. Sjödin, Harmonic balls and the two-phase Schwarz function, Complex Var. Elliptic Equ. 58 (2013), 837-852. Journal, arXiv

2012
L. Malý, Calderón-type theorems for operators with non-standard endpoint behavior on Lorentz spaces, Math. Nachr. 285 (2012), 1450-1465.
S.J. Gardiner and T. Sjödin, Two-phase quadrature domains, J. Anal. Math. 116 (2012), 335-354. Preprint

2011
A. Björn and H. Riesel Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), 1865-1866.
A. Björn and J. Björn, Power-type quasiminimizers, Ann. Acad. Sci. Fenn. Math. 36 (2011), 301-319. Journal
Z. Farnana, Pointwise regularity for solutions of double obstacle problems on metric spaces, Math. Scand. 109 (2011), 185-200.

2010
A. Björn, p-harmonic functions with boundary data having jump discontinuities and Baernstein's problem, J. Differential Equations 249 (2010), 1-36.
A. Björn, Cluster sets for Sobolev functions and quasiminimizers, J. Anal. Math. 112 (2010), 49-77.
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.
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.
J. Björn, Orlicz-Poincaré inequalities, maximal functions and $A_\Phi$-conditions, Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), 31-48.
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.
Z. Farnana, Convergence results for obstacle problems on metric spaces, J. Math. Anal. Appl. 371 (2010), 436-446.

2009
A. Björn, J. Björn, T. Mäkäläinen and M. Parviainen, Nonlinear balayage on metric spaces, Nonlinear Anal. 71 (2009), 2153-2171.
A. Björn and O. Martio, Pasting lemmas and characterizations of boundary regularity for quasiminimizers, Results Math. 55 (2009), 265-279.
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.
Z. Farnana, The double obstacle problem on metric spaces, Ann. Acad. Sci. Fenn. Math. 34 (2009), 261-277.

2008
A. Björn, A regularity classification of boundary points for p-harmonic functions and quasiminimizers, J. Math. Anal. Appl. 338 (2008), 39-47.
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.
J. Björn, Fine continuity on metric spaces, Manuscripta Math. 125 (2008), 369-381.
S. J. Gardiner and T. Sjödin, Convexity and the exterior inverse problem of potential theory, Proc. Amer. Math. Soc. 136 (2008), 1699-1703.

2007
A. Björn, Weak barriers in nonlinear potential theory, Potential Anal. 27 (2007), 381-387.
A. Björn and J. Björn, Approximations by regular sets and Wiener solutions in metric spaces, Comment. Math. Univ. Carolin. 48 (2007), 343-355.
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.
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.
S. J. Gardiner and T. Sjödin, Quadrature domains for harmonic functions, Bull. Lond. Math. Soc. 39 (2007), 586-590.
T. Sjödin, On the structure of partial balayage, Nonlinear Anal. 67 (2007), 94-102.
T. Sjödin, Approximation in the cone of positive harmonic functions, Potential Anal. 27 (2007), 271-280.

2006
A. Björn, Removable singularities for bounded p-harmonic and quasi(super)harmonic functions, Ann. Acad. Sci. Fenn. Math. 31 (2006), 71-95.
A. Björn, Removable singularities in weighted Bergman spaces, Czechoslovak Math. J. 56 (2006), 179-227.
A. Björn, A weak Kellogg property for quasiminimizers, Comment. Math. Helv. 81 (2006), 809-825.
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.
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.
A. Björn and N. Marola, Moser iteration for (quasi)minimizers on metric spaces, Manuscripta Math. 121 (2006), 339-366.
J. Björn, S. Buckley and S. Keith, Admissible measures in one dimension, Proc. Amer. Math. Soc. 134 (2006), 703-705.
T. Sjödin, Mother bodies of algebraic domains in the complex plane, Complex Var. Elliptic Equ. 51 (2006), 357-369.

2005
A. Björn, Characterizations of p-superharmonic functions on metric spaces, Studia Math. 169 (2005), 45-62.
A. Björn and H. Riesel, Table errata on "Factors of generalized Fermat numbers", Math. Comp. 74 (2005), 2099.
J. Björn and J. Onninen, Orlicz capacities and Hausdorff measures on metric spaces, Math. Z. 251 (2005), 131-146.

2003
A. Björn, Removable singularities for analytic functions in BMO and locally Lipschitz spaces, Math. Z. 244 (2003), 805-835.
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.
A. Björn, J. Björn and N. Shanmugalingam, The Perron method for p-harmonic functions, J. Differential Equations 195 (2003), 398-429.

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.
A. Björn, Properties of removable singularities for Hardy spaces of analytic functions, J. Lond. Math. Soc. 66 (2002), 651-670.
J. Björn, Boundary continuity for quasiminimizers on metric spaces, Illinois J. Math. 46 (2002), 383-403.
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.
J. Björn, Boundedness and differentiability for nonlinear elliptic systems, Trans. Amer. Math. Soc. 353 (2001), 4545-4565.
J. Björn, Poincar\'e inequalities for powers and products of admissible weights, Ann. Acad. Sci. Fenn. Math. 26 (2001), 175-188.
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.

2000
J. Björn, Lq-differentials for weighted Sobolev spaces, Michigan Math. J. 47 (2000), 151-161.
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.

1998
A. Björn Removable singularities for Hardy spaces, Complex Variables Theory Appl. 35 (1998), 1-25.
A. Björn, Removable singularities on rectifiable curves for Hardy spaces of analytic functions. Math. Scand. 83 (1998), 87-102.
A. Björn and Riesel, H., Factors of generalized Fermat numbers, Math. Comp. 67 (1998), 441-446 + 49 pp. of tables on micro-fiche.

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

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.

### 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.

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.

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

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.

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.
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.
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

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.

### Popular science articles

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 $\textbf{R}^{n}$ 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).
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 $k \cdot 2^q+1$ 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

Sofia Svensson, Lokala dimensioner och radiella vikter i $\textbf{R}^{n}$, 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).

Page responsible: anders.bjorn@liu.se
Last updated: 2017-07-17