On variational models for microstructures in shape-memory alloys

Shape-memory alloys are special materials that are able to remembertheir original shapes: Ifthey are deformed at low temperature, they return to their memorized shape when heated abovea critical temperature. Behind this effect is a solid-solid phase transition. The macroscopic behavi-or of these materials is closely linked to their microstructures. The latter are often modeled in thecontext of the calculus of variations by (possibly singularly perturbed) multi-well elastic energyfunctionals. In this talk, I shall discuss recent analytical progress on the resulting non-convex vec-torial energy minimization problems, including in particular results on solutions to related partialdifferential inclusion problems. This talk is based on joint works with S. Conti, M. Klar, A. Ruland,and C. Zillinger.