XXXV SCUOLA ESTIVA DI FISICA MATEMATICA
Ravello, September 13-18 2010

Gradient flows, optimal transport, and evolution PDEs

PDF slides of the lectures

• Gradient flows in linear spaces and their variational approximation
• A quick introduction to Optimal Transport
• Gradient flows and Wasserstein distance (I)
• Gradient flows and Wasserstein distance (II)
• Displacement convexity
• Application: the sticky particle system

Other references

• Jordan, Kinerlehrer, Otto The variational formulation of the Fokker-Planck equation SIAM J. Math. Anal. 29 (1998) 1-17
• Lecture notes of the course on Gradient flows and optimal transport
  Summer school on Optimal transportation: Theory and applications, Grenoble, June 2009.
• Luigi Ambrosio, Giuseppe Savaré Gradient Flows of Probability Measures
  Handbook of Evolution Equations Dafermos, C. and Feireisl, E. (ed.); Vol. 3, Elsevier (2006) 1-136
• C. Villani Optimal transport: Old and New Springer, 2009