Calculus of Variations and Geometric Measure Theory

F. Fleißner

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

created by fleißner on 29 Nov 2017
modified on 12 Feb 2020

[BibTeX]

Published Paper

Inserted: 29 nov 2017
Last Updated: 12 feb 2020

Journal: ESAIM:COCV
Year: 2016
Doi: 10.1051/cocv/2017035

ArXiv: 1603.02822 PDF

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.

Keywords: $\Gamma$-convergence, Gradient flows, Curves of maximal slope, minimizing movements