Segatti: A Variational Approach to Gradient Flows in Metric Spaces

Segatti, Antonio:
A Variational Approach to Gradient Flows in Metric Spaces
Bollettino dell'Unione Matematica Italiana Serie 9 6 (2013), fasc. n.3, p. 765-780, (English)
pdf (311 Kb), djvu (164 Kb). | MR 3202854

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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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Referenza completa

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Referenze Bibliografiche