Tuesday, 12 March 2019, 3 p.m. (sharp),

Prof. Filippo Santambrogio, Institut Camille Jordan, Université Claude Bernard - Lyon

at the conference room of IMATI-CNR in Pavia, will give a lecture titled:

Sobolev and BV estimates for the JKO scheme

as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).

At the end a refreshment will be organized.

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Abstract. I will show which kind of uniform BV and Sobolev estimates can be obtained for some equations which are gradient flows in the Wasserstein spaces and which range from Fokker-Planck to Keller-Segel systems or nonlinear diffusion. This will be based on optimal transport tools applied to the Jordan-Kinderlehrer-Otto scheme, using in particular on a new inequality (five-gradients-inequality) that we recently found in collaboration with De Philippis, Mészáros and Velichkov, in a work where we also provide an easy BV estimate for porous-medium-type diffusion. Similarly, in a recent work with Iacobelli and Patacchini we obtain and exploi (weighted) BV estimates for fast diffusion equations. The applications to various PDEs with linear diffusion, including Keller-Segel equations for chemotaxis are part of a joint ongoin work with Di Marino.