论文信息 - The heat equation on manifolds as a gradient flow in the Wasserstein space

The heat equation on manifolds as a gradient flow in the Wasserstein space

Nous etudions les flux gradients dans l'espace des mesures de probabilite sur une variete Riemannienne pas necessairement compacte. Dans ce but nous munissons l'espace de Wasserstein avec une sorte de structure Riemannienne. Si la courbure de Ricci de la variete est bornee inferieurement nous demontrons qu'il existe un flux gradient contractif pour l'entropie relative. Il est construit explicitement en utilisant une approximation variationelle discrete. De plus ses trajectoires Coincident avec les solutions a l'equation de la chaleur.

Matthias Erbar

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