Interactions Between Partial Differential Equations & Functional Inequalities

In recent years one can observe a rich and fruitful interplay between functional inequalities and nonlinear PDEs including: Entropy/entropy dissipation inequalities in nonlinear diffusions/reaction-diffusion models; Transport inequalities and relations to probabilities in Fokker-Planck like models; Variants of “Hardy-Littlewood-Sobolev” inequalitites and Keller-Segel models; Isoperimetric Inequalities and Flows like total variation, relativistic heat equations, p-Laplacians; Conservation laws and optimal transportation; Other challenging and exciting problems appear in fractional diffusions, or when one is dealing with H ̈ormander operators for example naturally related to analysis on groups or more generally in analysis on metric measure spaces.

The program will provide a broad platform for further exploration of these directions and beyond.

Workshop Interactions between Partial Differential Equations & Functional Inequalities 12 – 16 September