A global method for relaxation

A new method for the identification of the integral representation of a cla ss of functionals defined on BV(Omega; R-d) x A(Omega) (where A(Omega) repr esents the family of open subsets of Omega) is presented. Applications are derived, such as the integral representation of the relaxed energy in BV(Om ega; Rd) corresponding to a functional defined in W-1,W-1(Omega; R-d) with a discontinuous integrand with linear growth; relaxation and homogenization results in SBV(Omega: R-d) are recovered in the case where bulk and surfac e energies are present.