Stability of a class of action functionals depending on convex functions

TL;DR

This paper investigates the stability of a specific class of action functionals derived from convex functions' gradients, analyzing their behavior under Mosco convergence in general spaces.

Contribution

It introduces conditions ensuring the stability of these action functionals with respect to Mosco convergence, broadening understanding in convex analysis.

Findings

Established stability results under mild assumptions

Extended analysis to general underlying spaces

Provided conditions for Mosco convergence stability

Abstract

We study the stability of a class of action functionals induced by gradients of convex functions with respect to Mosco convergence, under mild assumptions on the underlying space.