Fractional Diffusion Equations. Theory on bounded domains

In this talk I will report on some of the progress made by the author and collaborators on the topic of nonlinear diffusion equations involving long distance interactions in the form of fractional Laplacian operators. In recent work with Bonforte and Sire we address the solution of Dirichlet problems in bounded domains, where the correct definition of what is the operator has a number of possible answers leading to different qualititative and quantitative results.

This seminar is organized within the PRIN 2012 Research project «Equazioni alle derivate
parziali di tipo ellittico e parabolico: aspetti geometrici, disuguaglianze collegate, e applicazioni
- Partial Differential Equations and Related Analytic-Geometric Inequalities» Grant Registration
number 2012TC7588_003, funded by MIUR – Project coordinator Prof. Filippo Gazzola