Equilibrium Configurations for Epitaxially Strained Films and Material Voids in Three-Dimensional Linear Elasticity

We extend the results about the existence of minimizers, relaxation, and approximation proven by Bonnetier and Chambolle (SIAM J Appl Math 62:1093-1121, 2002), Chambolle and Solci (SIAM J Math Anal 39:77-102, 2007) for an energy related to epitaxially strained crystalline films, and by Braides et al. (ESAIM Control Optim Calc Var 13:717-734, 2007) for a class of energies defined on pairs of function-set. We study these models in the framework of three-dimensional linear elasticity, where a major obstacle to overcome is the lack of any a priori assumption on the integrability properties of displacements. As a key tool for the proofs, we introduce a new notion of convergence for (d-1-rectifiable sets that are jumps of GSBDp functions, called sigma(p)(sym)-convergence.