In this note we report on a new variational principle for Gradient Flows in metric spaces. This new variational formulation consists in a functional defined on entire trajectories whose minimizers converge, in the case in which the energy is geodesically convex, to curves of maximal slope. The key point in the proof is a reformulation of the problem in terms of a dynamic programming principle combined with suitable a priori estimates on the minimizers. The abstract result is applicable to a large class of evolution PDEs, including Fokker Plack equation, drift diffusion and Heat flows in metric-measure spaces.

A variational approach to gradient flows in metric spaces,

SEGATTI, ANTONIO GIOVANNI
2013-01-01

Abstract

In this note we report on a new variational principle for Gradient Flows in metric spaces. This new variational formulation consists in a functional defined on entire trajectories whose minimizers converge, in the case in which the energy is geodesically convex, to curves of maximal slope. The key point in the proof is a reformulation of the problem in terms of a dynamic programming principle combined with suitable a priori estimates on the minimizers. The abstract result is applicable to a large class of evolution PDEs, including Fokker Plack equation, drift diffusion and Heat flows in metric-measure spaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/874636
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