Gamma-convergence of gradient flows on hilbert and metric spaces and applications

Abstract

We are concerned with γ-convergence of gradient ows, which is a notion meant to ensure that if a family of energy functionals depending of a parameter Γ-converges, then the solutions to the associated gradient ows converge as well. In this paper we present both a review of the abstract "theory" and of the applications it has had, and a generalization of the scheme to metric spaces which has not appeared elsewhere. We also mention open problems and perspectives.