The behaviour of microstructures with small shears of the austenite-martensite interface in martensitic phase transformations

Let W ì \BbbR²\Omega \subset \Bbb{R}^2 denote a bounded domain whose boundary ?W\partial \Omega is Lipschitz and contains a segment G₀\Gamma_0 representing the austenite-twinned martensite interface. We prove inf_{u ? W(W)} ò_W j(?u(x,y))dxdy=0\displaystyle{\inf_{{u\in \cal W}(\Omega)} \int_\Omega \varphi(\nabla u(x,y))dxdy=0}