Jan Müller (De)

English version

Dr. Jan-Steffen Müller (AG Fuchs)

4

Postanschrift:

jmueller@math.uni-sb.de

Forschungsinteressen

Variationsprobleme mit nicht-standard Wachstum sowie deren Anwendungen in Bildverarbeitung und Fluidmechanik
Regularitätstheorie elliptischer partieller Differentialgleichungen, Liouville- und Bernsteinsätze
Variationsprobleme mit einem Hintergrund in der geometrischen Maßtheorie

Veröffentlichungen:

A density result for Sobolev functions and functions of higher order bounded variation with additional integrability constraints, Ann. Acad. Sci. Fenn. Math. 41 (2016), 789-801. Preprint Version
(Mit M. Bidhauer, M. Fuchs, C. Tietz) On the solvability in Sobolev spaces and related regularity results for a variant of the TV-image recovery model: the vector-valued case, J. Elliptic Parabol. Equ. (2016) 2: 341-355. Preprint Version
(Mit M. Fuchs) A higher order TV-type variational problem related to the denoising and inpainting of images, Nonlinear Anal. 154 (2017), 122–147. Preprint Version
(Mit M. Fuchs, C. Tietz) Signal recovery via TV-type energies, Algebra i Analiz 29 (2017), no. 4, 159–195. Preprint Version
(Mit M. Fuchs, C. Tietz, J. Weickert) Convex regularization of multi-channel images based on variants of the TV-model, to appear in Complex Var. Elliptic Equ. Preprint Version
A coupled variational problem of linear growth related to the denoising and inpainting of images, J. Math. Sci. (2017) 224: 709-734 Preprint Version
(Mit M. Bildhauer, M. Fuchs, X. Zhong) On the local boundedness of generalized minimizers of variational problems with linear growth, to appear in Ann. Mat. Pura Appl. (1923-). Preprint Version
(Mit M. Fuchs) A remark on denoising of greyscale images using energy densities with varying growth rates, J. Math. Sci. (2018) 228: 705-722. Preprint Version
(Mit M. Bildhauer, M. Fuchs) A reciprocity principle for constrained isoperimetric problems and existence of isoperimetric subregions in convex sets, to appear in Calc. Var. Preprint Version

Preprints:

(Mit C. Tietz) Existence and almost everywhere regularity of generalized minimizers for a class of variational problems with linear growth related to image inpainting (2015)
(Mit M. Bildhauer, M. Fuchs) Existence and Regularity for Stationary Incompressible Flows with Dissipative Potentials of Linear Growth (2018)
(Mit M. Fuchs) A Liouville theorem for stationary incompressible fluids of von Mises type (2018)

Abschlussarbeiten

Dissertation: "Regularity Aspects of a Higher-Order Variational Approach to the Denoising and Inpainting of Images with TV-type Energies", Universität des Saarlandes, November 2017

Konferenzen und Vorträge:

February 8-12, 2016 School and Workshop "PDEs and applications", University of Naples "Federico II" (Minitalk)
July 11-15, 2016 The total variation flow and related nonlinear evolution problems,University of Salzburg (als Teilnehmer)
July 24, 2017 Vortrag "Optimale geometrische Strukturen" zum Tag der offenen Tür and der Universität des Saarlandes

Lehre

Als Lehrassistent:

Variationsrechnung, SoSe 2015
Höhere Mathematik für Ingenieure und Naturwissenschaftler I, WiSe 2015/16
Höhere Mathematik für Ingenieure und Naturwissenschaftler II, SoSe 2016
Differentialgeometrie, SoSe 2016
Analysis I, WiSe 2016/17
Analysis II, SoSe 2017
Analysis III, WiSe 2017/18