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 $(\chi,u)$ , where $\chi$ 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 symmetrized gradient as well as a perimeter term.