Gamma–closure of some classes of nonstandard convex integrands

Abstract

Within the framework of the theory of Γ-convergence for convex functionals with nonstandard coercivity and growth conditions, we study the inheritance of some properties (for example, strict convexity, differentiablility, and Δ2-property) of integrands under taking the Γ-closure. We focus on power integrands |ξ| p(x) with variable exponents. The results obtained are also of interest in the case of the Γ-convergence theory for standard functionals. Bibliography: 15 titles.