Prof. Dr. Stefan Müller

Hausdorff Chair / Associate Director of HIM

E-mail: stefan.mueller(at)
Phone: +49 228 73 62289
Room: 2.032
Location: Mathematics Center
Institute: Institute for Applied Mathematics
Max-Planck-Institute for Mathematics
Research Areas: Research Area B (Leader)
Research Area G
Mathscinet-Number: 663408

Academic Career


Diploma in Mathematics, University of Bonn


PhD, Heriot-Watt University, Edinburgh, Scotland, UK

1989 - 1990

Visiting Assistant Professor, Carnegie Mellon University, Pittsburgh, PA, USA

1990 - 1993

Postdoc, DFG Collaborative Research Centre SFB 256 “Nichtlineare partielle Differentialgleichungen”, University of Bonn

1993 - 1994

Visiting Member, Institute of Advanced Study, Princeton, NJ, USA


Professor, University of Freiburg


Professor, ETH Zürich, Switzerland

1996 - 2008

Director, Max Planck Institute for Mathematics in the Sciences, Leipzig

Since 2008

Professor (C4), University of Bonn

Since 2010

External Scientific Member, Max Planck Institute for Mathematics, Bonn

Research Profile

My goal is to develop mathematical methods to describe and understand multiscale problems and the formation, evolution and macroscopic effects of microstructure, in particular in advanced materials. I have always been fascinated by the subtle interplay of geometry, analysis, and physics in nonlinear elasticity, both for conventional and for phase-transforming materials. Results include a qualitatively new homogenization formula in nonlinear elastic materials [1], the first rigorous understanding of dimension reduction in nonlinear elasticity [5,6], and rigorous scaling laws for branching near austenite / martensite interfaces [2]. Implications for material design, e.g., for low-hysteresis shape memory alloys are explored in [8]. In turn estimates and constructions first discovered in elasticity led to new results in geometry [9] and rather striking counterexamples to Hilbert's 19th problem in PDE [10]. Other important areas are micromagnetics, where a simple, yet subtle, energy functional describes a huge variety of magnetization patterns on very different scales [7] and plasticity [4].
Recently I have begun work on understanding the relation between atomistic and continuum theory of solids through statistical mechanics and rigorous renormalization.

Research Projects and Activities

DFG Collaborative Research Centre SFB 1060 “The Mathematics of Emergent Effects”

DFG Research Group FOR 797 “Microplast - Analysis and computation of microstructure in finite plasticity”

Contribution to Research Areas

Research Area B
Expertise in nonconvex problems in the calculus of variations and their applications to material microstructure, including recent extensions to atomistic models as well as in a broad range of rigorous multiscale methods, including homogenization [1], singular perturbations [2,3], and <br>Gamma-convergence [4,5,6,7].
Research Area G
Statistical mechanics of solids and thermodynamic limits through rigorous renormalization group methods.
Relations between variational methods and small noise limits through capacity estimates and the theory of large deviations.

Selected Publications

[1] Stefan Müller
Homogenization of nonconvex integral functionals and cellular elastic materials
Arch. Rational Mech. Anal. , 99: (3): 189--212
ISSN: 0003-9527
DOI: 10.1007/BF00284506
[2] Robert V. Kohn, Stefan Müller
Surface energy and microstructure in coherent phase transitions
Comm. Pure Appl. Math. , 47: (4): 405--435
ISSN: 0010-3640
DOI: 10.1002/cpa.3160470402
[3] Stefan Müller
Singular perturbations as a selection criterion for periodic minimizing sequences
Calc. Var. Partial Differential Equations , 1: (2): 169--204
ISSN: 0944-2669
DOI: 10.1007/BF01191616
[4] Sergio Conti, Adriana Garroni, Stefan Müller
Singular kernels, multiscale decomposition of microstructure, and dislocation models
Arch. Ration. Mech. Anal. , 199: (3): 779--819
ISSN: 0003-9527
DOI: 10.1007/s00205-010-0333-7
[5] Gero Friesecke, Richard D. James, Stefan Müller
A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
Arch. Ration. Mech. Anal. , 180: (2): 183--236
ISSN: 0003-9527
DOI: 10.1007/s00205-005-0400-7
[6] Gero Friesecke, Richard D. James, Stefan Müller
A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
Comm. Pure Appl. Math. , 55: (11): 1461--1506
ISSN: 0010-3640
DOI: 10.1002/cpa.10048
[7] Antonio DeSimone, Robert V. Kohn, Stefan Müller, Felix Otto
A reduced theory for thin-film micromagnetics
Comm. Pure Appl. Math. , 55: (11): 1408--1460
ISSN: 0010-3640
DOI: 10.1002/cpa.3028
[8] Z.~Y.~Zhang , R.~D.~James , S.~Müller
Energy barriers and hysteresis in martensitic phase transformations
Acta Materialia , 57: : 4332--4352
[9] Alexandre Freire, Stefan Müller, Michael Struwe
Weak convergence of wave maps from (1+2)-dimensional Minkowski space to Riemannian manifolds
Invent. Math. , 130: (3): 589--617
ISSN: 0020-9910
DOI: 10.1007/s002220050195
[10] S. Müller, V. Sverák
Convex integration for Lipschitz mappings and counterexamples to regularity
Ann. of Math. (2) , 157: (3): 715--742
ISSN: 0003-486X
DOI: 10.4007/annals.2003.157.715

Publication List


• Archive of Rational Mechanics and Analysis
• Interfaces and Free Boundaries
• Journal of Analysis and its Applications
• M3AS



Prize of the European Mathematical Society


Max Planck Research Award (jointly with V. Sverák)


Member of the Berlin-Brandenburg Academy of Sciences and Humanities


Collatz Prize of CICIAM


Leibniz Prize


Member of the Leopoldina (German National Academy of Sciences)


Heinz Gumin Prize Mathematics of the Carl Friedrich von Siemens Foundation


Member of the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts


Member of the Academia Europaea

Selected Invited Lectures


Plenary, German Mathematical Society


ECM, Budapest, Hungary


Austrian Mathematical Society


Andrejewski Lectures, Berlin


ICM, Berlin


GAMM, Bremen


ICIAM, Edinburgh, Scotland, UK


Ordway Lectures, Minneapolis, MN, USA


Landau Lectures, Jerusalem, Israel


Gauss Lecture, Bremen


ICMP, Rio de Janeiro, Brasil


Annual Meeting of Leopoldina (German National Academy of Sciences)


Bernd Kirchheim (2001), now Professor, University of Leipzig

Georg Dolzmann (2002), now Professor, University of Regensburg

Sergio Conti (2004), now Professor, University of Bonn

Selected PhD students

Anja Schlömerkemper (2002): “Magnetic Forces in Discrete and Continuous Systems”,
now Professor, University of Würzburg

Christof Melcher (2002): “Néel walls and regularity in thin film micromagnetics”,
now Professor, RWTH Aachen University

László Székelyhidi Jr. (2004): “Elliptic Regularity versus Rank-One Convexity”,
now Professor, University of Leipzig

Bernd Schmidt (2006): “Effective theories for thin elastic films”,
now Professor, University of Augsburg

Supervised Theses

  • PhD theses: 14, currently 2
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