×

A global method for relaxation. (English) Zbl 0921.49004

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)

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI