LECTURE NOTES ON GRADIENT FLOWS AND OPTIMAL TRANSPORT

Sara Daneri (1) , Giuseppe Savaré (2)

1 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
2 Dipartimento di matematica F. Casorati

We present a short overview on the strongest variational formulation for gradient flows of geodesically $\lambda$-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School ``Optimal transportation: Theory and applications'' in Grenoble during the week of June 22-26, 2009.

Domaines: Analyse classique [math.CA]; Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Sara Daneri, Giuseppe Savaré. LECTURE NOTES ON GRADIENT FLOWS AND OPTIMAL TRANSPORT. 2009. ⟨hal-00519401⟩