A moving mask hypothesis to select physically relevant microstructures

Martensitic transformations are phase transitions between different crystalline states occurring in certain alloys. These are often characterised by complex microstructures, which have been widely studied in the context of the calculus of variations. However, it may occur that infinitely many minimisers exist, and it is an open problem how to select the physically relevant ones. In this talk I present a moving mask hypothesis that can be used as a selection mechanism for physically relevant microstructures in thermally induced martensitic phase transitions. The moving mask hypotheses allows to prove a rigidity result for the two-well problem, and to better understand the importance of the cofactor conditions, particular conditions of supercompatibility between phases, which are believed to influence reversibility.