Geodesic
A Variational Approach to Gradient Flows in Metric Spaces
Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 765-780 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{BUMI_2013_9_6_3_a18,
     author = {Segatti, Antonio},
     title = {A {Variational} {Approach} to {Gradient} {Flows} in {Metric} {Spaces}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {765--780},
     year = {2013},
     volume = {Ser. 9, 6},
     number = {3},
     mrnumber = {3202854},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a18/}
}
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Segatti, Antonio. A Variational Approach to Gradient Flows in Metric Spaces. Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 765-780. http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a18/