Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
3/1997

Microstructures, phase transitions and geometry

Stefan Müller

Abstract

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.

Received:
Feb 27, 1997
Published:
Feb 27, 1997

Related publications

inBook
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)