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Santambrogio: Sobolev and BV estimates for the JKO scheme

Santambrogio:
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 exploit (weighted) BV estimates for fast diffusion equations. The applications to various PDEs with linear diffusion, including Keller-Segel equations for chemiotaxis are part of a joint ongoing work with Di Marino.
http://cvgmt.sns.it/seminar/686/
When
Mon Apr 15, 2019 12:45pm – 1:45pm Coordinated Universal Time
Where
Sala Riunioni del Dipartimento di Matematica, Università di Pisa, (map)