A global method for relaxation

Abstract: "A new method for the identification of the integral representation of some class of functionals defined on BV([omega];R[superscript d])xA([omega]) (where A([omega]) represents a family of open subsets of [omega]) is presented. Applications are derived, such as the integral representation of the relaxed energy in BV([omega];R[superscript d]) corresponding to a functional defined in W[superscript 1,1]([omega];R[superscript d]) with a discontinuous integrand with linear growth; relaxation and homogenization results in SBV([omega];R[superscript d]) are recovered in the case where bulk and surface energies are present."