Bouchitté, Guy; Fonseca, Irene; Mascarenhas, Luisa A global method for relaxation. (English) Zbl 0921.49004 Arch. Ration. Mech. Anal. 145, No. 1, 51-98 (1998). From the author’s abstract: “A new method for the identification of the integral representation of a class of functionals defined on \(\text{BV} (\Omega,R^d) \times{\mathcal A}(\Omega)\) (where \({\mathcal A}(\Omega)\) represents the family of open subsets of \(\Omega)\) is presented. Applications are derived, such as the integral representation of the relaxed energy in \(\text{BV}(\Omega,R^d)\) corresponding to a functional defined in \(W^{1,1} (\Omega, R^d)\) with discontinuous integrand with linear growth; relaxation and homogenization results in \(\text{SBV}(\Omega, R^d)\) are recovered in the case where bulk and surface energies are present”. Reviewer: R.Schianchi (Roma) Cited in 3 ReviewsCited in 60 Documents MSC: 49J45 Methods involving semicontinuity and convergence; relaxation 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics Keywords:SBV; special functions of bounded variation; homogenization PDFBibTeX XMLCite \textit{G. Bouchitté} et al., Arch. Ration. Mech. Anal. 145, No. 1, 51--98 (1998; Zbl 0921.49004) Full Text: DOI