Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
Sylvia Serfaty - UPMC Univ Paris 06, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, F-75005, France (email)
Abstract: We are concerned with $\Gamma$-convergence of gradient flows, which is a notion meant to ensure that if a family of energy functionals depending of a parameter $\Gamma$-converges, then the solutions to the associated gradient flows 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.
Keywords: Gradient flow, Gamma-convergence, Ginzburg-Landau equation, Allen-Cahn equation, Cahn-Hilliard equation, Mullins-Sekerka evolution.
Received: May 2009; Revised: July 2010; Published: September 2011.
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