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MiS Preprint
12/1998
Lipschitz minimizers of the 3-well problem having gradients of bounded variation
Bernd Kirchheim
Abstract
We consider solutions of the three well problem. These are maps u satisfying $\nabla u \in SO(3)A^1 \cup SO(3)A^2 \cup SO(3)A^3$ a.e. in $\Omega \subset R^3$ where the $A^i$ are the diagonal matrices representing the cubic to tetragonal transformation. It is known that such maps can behave rather irregular. Under the additional assumption that the phase sets $E^i=\{x; \nabla u (x) \in SO(3) A^i \}$ are of finite perimeter we conclude that u is locally a function of one variable only.
