Speaker: Nicola Garofalo (University of Padova)
Title: Nonlocal Sobolev and isoperimetric inequalities for a class of non-symmetric and non-doubling semigroups
Abstract: In his seminal 1934 paper on Brownian motion and the theory of gases Kolmogorov introduced a second order evolution equation which displays many challenging features. Despite the large amount of work done by many people over the past thirty years, some basic questions presently remain unsettled such as Hardy-Littlewood-Sobolev and Isoperimetric inequalities, a Calderόn-Zygmund theory, and the study of local and nonlocal minimal surfaces. In this lecture I will present a fractional calculus adapted to a class of equations modelled on Kolmogorov’s, and using such calculus I will discuss some interesting developments in the above program.