Relaxation of singular functionals defined on Sobolev spaces
Hafedh Ben Belgacem · ESAIM Control Optimisation and Calculus of Variations · 2000
In this paper, we consider a Borel measurable function on the space of matrices taking the value , such that its rank-one-convex envelope is finite and satisfies for some fixed : where . Let be a given regular bounded open domain of . We define on the functional Then, under some technical restrictions on , we show that the relaxed functional for the weak topology of has the integral representation: where for a given function , denotes its quasiconvex envelope.