Approximation of a laminated microstructure for a rotationally invariant, double well energy density

We give error estimates for the approximation of a laminated microstructure which minimizes the energy \(\int_\Omega \phi(\nabla v(x))\,dx\) for a rotationally invariant, double well energy density \(\phi(A)\). We present error estimates for the convergence of the deformation in \(L^2,\) the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient.

Authors and Affiliations

1. School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA; e-mail: luskin@math.umn.edu, , , , , , US

   Mitchell Luskin

Received July 25, 1995 / Revised version received November 20, 1995

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