Marvin Weidner (Barcelona)
Abstract: The celebrated De Giorgi-Nash-Moser theory establishes Hölder regularity of solutions to second order equations in divergence form without any regularity assumptions on the coefficients. This result was a key ingredient in the resolution of Hilbert's XIXth problem in the 1950s. An important contribution to the theory was made by Moser who established a Harnack inequality for solutions to such equations.
Recently, there was a huge interest in the study of similar regularity estimates for solutions to nonlocal equations governed by integro-differential operators that are modeled upon the fractional Laplacian. In this talk, we will give an overview of the corresponding theory for nonlocal equations. We will focus on the main difficulties arising from the long range interactions, that lie in the nature of nonlocal models. Moreover, we will explain our recent results on the nonlocal parabolic Harnack inequality and Hölder regularity estimates, which complete the regularity program for linear nonlocal equations with bounded measurable coefficients.
This talk is based on a joint work with Moritz Kaßmann
