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

DOI10.1051/cocv/2017035zbMath1442.49017arXiv1603.02822OpenAlexW2962840640MaRDI QIDQ5107932

Florentine Catharina Fleißner

Publication date: 29 April 2020

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.02822

zbMATH Keywords

relaxation\(\Gamma\)-convergencegradient flowsminimizing movementscurves of maximal slope

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Iterative procedures involving nonlinear operators (47J25) Methods involving semicontinuity and convergence; relaxation (49J45) Discrete approximations in optimal control (49M25)

Related Items (4)

Minimal solutions to generalized \(\Lambda \)-semiflows and gradient flows in metric spaces ⋮ An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems ⋮ Perturbed minimizing movements of families of functionals ⋮ A minimizing Movement approach to a class of scalar reaction–diffusion equations

Cites Work

• Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
• Asymptotic expansions by \(\Gamma \)-convergence
• An introduction to \(\Gamma\)-convergence
• Variational convergence of gradient flows and rate-independent evolutions in metric spaces
• \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems
• PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW
• Evolution equations with lack of convexity
• Gradient flows of non convex functionals in Hilbert spaces and applications
• Lecture Notes on Gradient Flows and Optimal Transport
• Gamma-convergence of gradient flows with applications to Ginzburg-Landau
• Curvature-Driven Flows: A Variational Approach
• On the heat flow on metric measure spaces: existence, uniqueness and stability
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