Calculus of Variations and Geometric Measure Theory

V. Crismale - M. Friedrich

Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity

created by crismale on 15 Oct 2019
modified on 15 May 2020


Published Paper

Inserted: 15 oct 2019
Last Updated: 15 may 2020

Journal: Arch. Rational Mech. Anal.
Volume: 237
Pages: 1041-1098
Year: 2020

ArXiv: 1910.03845 PDF


We extend the results about existence of minimizers, relaxation, and approximation proven by Chambolle et al. in 2002 and 2007 for an energy related to epitaxially strained crystalline films, and by Braides, Chambolle, and Solci in 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 $GSBD^p$ functions, called $\sigma^p_{\mathrm{sym}}$-convergence.