Inserted: 18 dec 2012
Last Updated: 13 sep 2016
Journal: proceedings of the Bourbaki seminar
I have been asked to present this topic at the Séminaire Bourbaki of January 19th, 2013. This is the text accompanying the talk that I will give.
I apologize for the text being in French, but Nicolas Bourbaki told me that he has "une préférence pour le français"...
Finally, let me thank Nicola Gigli for many clarifying discussions about the topic and precise improvement suggestions on the text.
The text aims to be a (personal) synthesis of the works by Ambrosio, Gigli and Savaré on the wide topic of gradient flows on metric space. It contains three parts: the general theory in metric spaces, the case of functionals on the Wasserstein space, the heat flow on metric measure spaces.
Keywords: gradient flows, metric measure spaces, Wasserstein, evolution PDEs, heat flow