Gamma-convergence and relaxations for gradient flows in metric spaces: a minimizing movement approach

2016/03/09 by Florentine Catharina Fleißner, Fleißner, Florentine · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1603.02822

openalex publication_date 2016/03/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present new abstract results on the interrelation between the minimizing movement scheme for gradient flows along a sequence of Gamma-converging functionals and the gradient flow motion for the corresponding limit functional, in a general metric space. We are able to allow a relaxed form of minimization in each step of the scheme, and so we present new relaxation results too.

Cited by

• Mosco convergence framework for singular limits of gradient flows on Hilbert spaces with applications

Related

• A relation between Gamma convergence of functionals and their associated gradient flows
• Gradient flows and Evolution Variational Inequalities in metric spaces. I: structural properties
• On gradient descent-ascent flows in metric spaces
• Gamma-convergence of integral functionals depending on vector-valued functions over parabolic domains
• Weighted Energy-Dissipation principle for gradient flows in metric spaces