Lower Semicontinutty of Integral Functionals

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

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...

A 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.

GENERALIZED 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...

A Theorem on Lower Semicontinuity of Integral Functionals

A general lower semicontinuity theorem, in which not only mappings uM and PM but also the integrands fM depend on M , is proved for integrands f, fM under certain general hypotheses including that f(x, u, P ) is convex respect to P and fM converge to f locally uniformly, but fM (x, u, P ) are not required to be convex respect to P and fM (x, ·, ·) do not even need to be lower semicontinuous. So...