MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Microstructures, phase transitions and geometry

Stefan Müller


Microstructures are abundant in nature and often crucially influence a material's or system's behaviour. The mathematical analysis of microstructures leads to simply stated but challenging mathematical problems and involves an interaction of a variety of mathematical fields including the calculus of variations, partial differential equations, real and functional analysis and differential geometry.
This paper outlines some of the basic problems using the example of crystal microstructure in solid-solid phase transitions and discusses recent progress on exact solutions (obtained by Gromov's method of convex integration) and on the interaction of surface energy and fine scale geometry.


Related publications

1998 Repository Open Access
Stefan Müller

Microstructures, phase transitions and geometry

In: European Congress of Mathematics : Budapest, July 22 - 26, 1996. Vol. 2 / A. Balog... (eds.)
Basel : Birkhäuser, 1998. - pp. 92-115
(Progress in mathematics (Boston, Mass.) ; 169)