Relaxation for an optimal design problem in $BD(Ω)$

Abstract

We obtain a measure representation for a functional arising in the context of optimal design problems under linear growth conditions. The functional in question corresponds to the relaxation with respect to a pair (χ, u), where χ is the characteristic function of a set of finite perimeter and u is a function of bounded deformation, of an energy with a bulk term depending on the symmetrised gradient as well as a perimeter term.