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

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