A variational principle for gradient flows in metric spaces

DOI10.1016/j.crma.2011.11.002zbMath1236.49065OpenAlexW2145195932MaRDI QIDQ654538

Antonio Segatti, Giuseppe Savaré, Ulisse Stefanelli, Riccarda Rossi

Publication date: 28 December 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2011.11.002

zbMATH Keywords

dynamic programming principlecurves of maximal slopegeodesically convex energiesgradient-flow evolution in metric spacesHamilton--Jacobi equationnonlinear evolution PDEs

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Dynamic programming in optimal control and differential games (49L20) Nonlinear systems in control theory (93C10) Optimality conditions for problems in abstract spaces (49K27) Fokker-Planck equations (35Q84)

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Variational resolution of outflow boundary conditions for incompressible Navier–Stokes ⋮ A new minimum principle for Lagrangian mechanics ⋮ Existence of evolutionary variational solutions via the calculus of variations ⋮ Dynamic Perfect Plasticity as Convex Minimization ⋮ A variational approach to doubly nonlinear equations ⋮ Variational methods for evolution. Abstracts from the workshop held November 12--18, 2017 ⋮ A variational approach to Navier–Stokes ⋮ Weighted energy-dissipation approach to doubly nonlinear problems on the half line ⋮ Elliptic-regularization of nonpotential perturbations of doubly-nonlinear gradient flows of nonconvex energies: A variational approach ⋮ Stochastic PDEs via convex minimization ⋮ A variational approach to the mean field planning problem ⋮ Weighted energy-dissipation principle for gradient flows in metric spaces

Cites Work

• Unnamed Item
• Weighted energy-dissipation functionals for doubly nonlinear evolution
• Minimum principles for the trajectories of systems governed by rate problems
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Weighted energy-dissipation functionals for gradient flows
• A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems
• Elliptic regularization and partial regularity for motion by mean curvature
• A discrete variational principle for rate-independent evolution

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