Matematiska institutionen## Johan ThimLinköpings universitet 581 83 Linköping E-mail: jothi@mai.liu.se Phone: 013 - 28 16 89 Fax: 013 - 10 07 46 Office: Rum 677, A-korridoren, 1 tr. (B-huset) Research gate |

I am a senior lecturer at the department of Mathematics, Linköping University. I work at the division for pure and applied mathematics (MTM).

## Research Areas

My main area of research is analysis and partial differential equations, in particular on domains with minimal smoothness assumptions. The aim is to develop asymptotic methods for dealing with nonsmooth domains when solving partial differential equations. The study of regularity properties of solutions is a central problem in PDE theory, and developing tools is very important since not much is known for nonsmooth domains. I also have a large interest in mathemical history of the more modern type (my master's thesis dealt with the history of continuous nowhere differentiable functions). Some of the topics I'm currently working on includes the following.

- Local estimates for Riesz potentials on nonsmooth surfaces.
- Local estimates for solutions to elliptic equations near bad points at the boundary; asymptotic methods.
- Hadamard type asymptotics for eigenvalues of elliptic operators under domain perturbations.
- Continuous nowhere differentiable functions (historical).

## Publications

### Pre-prints:

2014: Hadamard Type Asymptotics for Eigenvalues of the Neumann Problem for Elliptic Operators

### New publications:

2015: Asymptotics of Hadamard Type for Eigenvalues of the Neumann Problem on C1-domains for Elliptic Operators

2014: Asymptotics and inversion of Riesz potentials through decomposition in radial and spherical parts

### Publications (diva-extraction):

The publication list is extracted from the DiVA - Academic Archive Online - publishing system. The extraction software is developed by Johan Wiklund.

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## Journal papers

2017

Fredrik Berntsson, Anna Orlof, Johan Thim,
"Error Estimation for Eigenvalues of Unbounded Linear Operators and an Application to Energy Levels in Graphene Quantum Dots",
Numerical Functional Analysis and Optimization,
38(3):
293-305, 2017.

2016

Vladimir Kozlov, Johan Thim,
"Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators",
Journal of Spectral Theory,
6(1):
99-135, 2016.

Johan Thim,
"Asymptotics and inversion of Riesz potentials through decomposition in radial and spherical parts",
Annali di Matematica Pura ed Applicata,
195(2):
323-341, 2016.

2015

Johan Thim,
"ASYMPTOTICS OF HADAMARD TYPE FOR EIGENVALUES OF THE NEUMANN PROBLEM ON C-1-DOMAINS FOR ELLIPTIC OPERATORS",
Analysis & PDE,
8(7):
1695-1706, 2015.

Johan Thim,
"Two Weight Estimates for the Single Layer Potential on Lipschitz Surfaces with Small Lipschitz Constant",
Potential Analysis,
43(1):
79-95, 2015.

2014

Vladimir Kozlov, Johan Thim, Bengt-Ove Turesson,
"Single layer potentials on surfaces with small Lipschitz constants",
Journal of Mathematical Analysis and Applications,
418(2):
676-712, 2014.

2010

Vladimir Kozlov, Johan Thim, Bengt-Ove Turesson,
"A Fixed Point Theorem in Locally Convex Spaces",
Collectanea Mathematica (Universitat de Barcelona),
61(2):
223-239, 2010.

2009

Johan Thim, Vladimir Kozlov, Bengt-Ove Turesson,
"Riesz Potential Equations in Local L

^{p}-spaces.", Complex Variables and Elliptic Equations, 54(2): 125-151, 2009.## Theses

2009

Johan Thim,
"Simple Layer Potentials on Lipschitz Surfaces: An Asymptotic Approach",
Linköping Studies in Science and Technology. Dissertations,
No. 1235,
2009.

### Monographs:

- Master's thesis (Continuous Nowhere Differentiable Functions)
- PhD thesis (only introduction in fulltext)

## Teaching

### Undervisning och examination (aktuellt):

- TATM79: Matematisk grundkurs (Y, Yi, MED, Mat, FyN, Frist)
- TATA42: Envariabelanalys 2 (D, IT, KB, TB)
- 91MA11/91MA17/92MA11/92MA17: Algebra

### Undervisning och examination (tidigare):

- 92MA31/92MA37: Matematisk statistik
- TAMS79: Matematisk statistik I
- TATA68: Matematisk grundkurs
- 9MA241/9MA341: Matematisk statistik
- TATA09: Flervariabelanalys
- TNG006 (Campus Norrköping): Matematisk statistik (avaktiverad)

## Course materials

### Blandat kursmaterial (mostly in Swedish):

- Kort sammanfattning/ordlista för linjär algebra i 2D/3D (2009/2017).
- Envariabelanalys del 2 (2016)
- Matematisk grundkurs -- Algebra (2016)
- Sannolikhetslära och matematisk statistik (2013)

Sidansvarig: johan.thim@liu.se

Senast uppdaterad: 2017-09-25