Prof. Dr. Stefan Müller

Hausdorff Chair / Associate Director of HIM

E-mail: stefan.mueller(at)
Phone: +49 228 73 62289
Fax: +49 228 73 62384
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

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 Center 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, the first rigorous understanding of dimension reduction in nonlinear elasticity [2,3], and rigorous scaling laws for branching near austenite / martensite interfaces [1]. Implications for material design, e.g., for low-hysteresis shape memory alloys are explored in [5]. In turn estimates and constructions first discovered in elasticity led to new results in geometry and rather striking counterexamples to Hilbert's 19th problem in PDE [6].
Recent and ongoing work addresses the influence of microscopic defects on effective material behaviour, e.g. in plasticity [7,8] as well as scaling levels and pattern formation in thin elastic sheets [9]. In both areas the rigidity estimates of [3] play a crucial role. I have also begun to work on the relation between atomistic and continuum theory of solids through statistical mechanics and rigorous renormalization.

Research Projects and Activities

Coordinator of the DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”

Principal Investigator of the DFG Cluster of Excellence “Hausdorff Center for Mathematics”

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, singular perturbations [1], and <br>Gamma-convergence [2,3,4].
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] Robert V. Kohn, Stefan Müller
Surface energy and microstructure in coherent phase transitions
Comm. Pure Appl. Math. , 47: (4): 405--435
[2] 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
[3] 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
[4] Antonio DeSimone, Robert V. Kohn, Stefan Müller, Felix Otto
A reduced theory for thin-film micromagnetics
Comm. Pure Appl. Math. , 55: (11): 1408--1460
[5] Zhiyong Zhang, Richard D. James, Stefan Müller
Energy barriers and hysteresis in martensitic phase transformations
Acta Materialia , 57: (15): 4332--4352
[6] S. Müller, V. \v Sverák
Convex integration for Lipschitz mappings and counterexamples to regularity
Ann. of Math. (2) , 157: (3): 715--742
[7] Sergio Conti, Adriana Garroni, Stefan Müller
Dislocation microstructures and strain-gradient plasticity with one active slip plane
J. Mech. Phys. Solids , 93: : 240--251
[8] Stefan Müller, Lucia Scardia, Caterina Ida Zeppieri
Geometric rigidity for incompatible fields, and an application to strain-gradient plasticity
Indiana Univ. Math. J. , 63: (5): 1365--1396
[9] Stefan Müller, Heiner Olbermann
Conical singularities in thin elastic sheets
Calc. Var. Partial Differential Equations , 49: (3-4): 1177--1186
[10] Olga Dmitrieva, Patrick Dondl, Stefan Müller, Dierk Raabe
Lamination microstructure in shear deformed copper single crystals
Acta Materialia , 57: (12): 3439--3449

Publication List

MathSciNet Publication List (external link)

ArXiv Preprint List (external link)


• Archive of Rational Mechanics and Analysis
• Control, Optimisation and Calculus of Variations
• Forum of Mathematics, Pi and Sigma



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 ICIAM


Leibniz Prize


Member of the Leopoldina (German National Academy of Sciences)


Heinz Gumin Prize for 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


Teaching Award University of Bonn

Selected Invited Lectures


Plenary speaker, German Mathematical Society, Duisburg


European Congress of Mathematics, Budapest, Hungary


Austrian Mathematical Society


Andrejewski Lectures, Berlin


International Congress of Mathematicians, Berlin


Annual Meeting of 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)


Conference “New developments in elasticity: the legacy of Robert Hocke”, Oxford, England, UK


Lecture series “Mathematical problems in thin elastic sheets”, Cetraro, Italy


Conference “Geometric nonlinear analysis”, ETH Zürich, Switzerland


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

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

Barbara Zwicknagl (2011): “Mathematical analysis of microstructures and low hysteresis shape memory alloys”,
now Junior Professor, University of Würzburg

Supervised Theses

  • PhD theses: 19, currently 3
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