The two well problem for piecewise affine maps
The two well problem for piecewise affine maps
In the \textit{two-well problem} we look for a map $u$ which satisfies Dirichlet boundary conditions and whose gradient $Du$ assumes values in $SO\left( 2\right) A\cup SO\left( 2\right) B=\mathbb{S}_{A}\cup \mathbb{S}_{B},$ for two given invertible matrices $A,B$ (an element of $SO\left( 2\right) A$ is of the form $RA$ where $R$ is a …