Niveau: Supérieur, Doctorat, Bac+8
Workshop Optimal Transport: Theory and Appli ations Fourier Institute (Grenoble I, Fran e) June 29th-July 3rd Titles and abstra ts of the talks F. Bollet (Paris-Dauphine) Phi-entropy inequalities and Fokker-Plan k equations The onvergen e to equilibrium for Fokker-Plan k type diusion equations an be studied by means of fun tional inequalities su h as the Poin aré and logarithmi Sobolev inequalities. We present this link and we derive and study a family of Phi- entropy inequalities: they provide an interpolation between these two fun tional inequalities and an make the onvergen e to equilibrium more pre ise. This is a joint work with I. Gentil. Y. Brenier (Ni e) Optimal transport, onve tion theory and semi-geostrophi equations There are several well known links between optimal transport and uid me han- i s. For instan e, the polar fa torization of maps is dire tly related to the time dis retization of the Euler equations (in the Arnold style). Another link has been re ently established with onve tion theory, the entral theory of geophysi al ows. The rst step is an interpretation of the Angenent-Haker-Tannenbaum model for optimal transport as a onve tion model in porous media (des ribed by the Dar y- Boussinesq equations).
- tions has
- tion
- unexpe ted
- image transfer
- optimal transport
- inequalities via lyapunov onditions
- stru ture
- inequalities
- transportation problem