APDE seminar @UPV/EHU: The Cauchy-Dirichlet Problem for singular nonlocal diffusions on bounded domains

Abstract

We will discuss about homogeneous Cauchy-Dirichlet Problem for a  nonlocal fast diffusion equation posed on a bounded Euclidean domain.  The prototype equation is the "Fractional Fast Diffusion Equation", when L is one of the three possible Dirichlet Fractional Laplacians on Ω. The main results shall provide a complete basic theory for solutions to (CDP): existence and uniqueness in the biggest class of data known so far; sharp smoothing estimates; extinction rates and regularity of solutions.