Integral Representation for a Class of C-convex Functionals
نویسندگان
چکیده
In view of the applications to the asymptotic analysis of a family of obstacle problems, we consider a class of convex local functionals F (u,A), defined for all functions u in a suitable vector valued Sobolev space and for all open sets A in R. Sufficient conditions are given in order to obtain an integral representation of the form F (u,A) = ∫ A f(x, u(x)) dμ+ν(A), where μ and ν are Borel measures and f is convex in the second variable. Ref. S.I.S.S.A. 71/M (May 92) Integral representation for a class of C-convex functionals 1
منابع مشابه
A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces
متن کامل
Continuous essential selections and integral functionals
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as fully lower semicontinuous closed convex-valued mappings that arise in variational analysis and optimization of integral functionals. The characterization allo...
متن کاملGENERALIZED POSITIVE DEFINITE FUNCTIONS AND COMPLETELY MONOTONE FUNCTIONS ON FOUNDATION SEMIGROUPS
A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...
متن کاملA Derivation Formula for Convex Integral Functionals Deened on Bv ()
We show that convex lower semicontinuous functionals deened on functions of bounded variation are characterized by their minima, and we prove a derivation formula which allows an integral representation of such functionals. Applications to relaxation and homogenization are given.
متن کاملA generalized form of the Hermite-Hadamard-Fejer type inequalities involving fractional integral for co-ordinated convex functions
Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.
متن کامل