Research

Stefan Müller's research 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. He has 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 and rigorous scaling laws for branching near austenite/martensite interfaces. This led to new results in geometry and counterexamples to Hilbert's 19th problem in partial differential equations.