| Abstract: |
| In this talk I present a new, self-contained compactness argument for a discrete multi-well problem with $SO(n)$ symmetry of the type which typically arises in applications to phase transformations in physics. As the main ingredients I discuss a spin-type argument and a reduction of the compatible multi-well problem to an incompatible single-well problem. Relying on the formulation as an incompatible single-well problem, I then deduce compactness and an accompanying structure result. This result for instance applies to martensitic phase transformations in the surface energy regime, but also remains valid for a much more general class of phase transformation problems, in which the ground states can for instance be periodic. The talk is based on joint work with G. Kitavtsev, G. Lauteri and S. Luckhaus. |
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