Harnack Inequalities for Parabolic Nonlocal Equations

This lecture explores the study of regularity results for solutions to nonlocal equations governed by operators modeled upon the fractional Laplacian, focusing specifically on time-dependent nonlocal equations with bounded measurable coefficients. Discover recent findings on the nonlocal parabolic Harnack inequality and learn about purely nonlocal phenomena, including the failure of Hölder estimates for certain weak solutions and the validity of time-insensitive Harnack estimates. The presentation draws from joint research conducted with Moritz Kassmann and Naian Liao, and was delivered as part of the Workshop on "Degenerate and Singular PDEs" at the Erwin Schrödinger International Institute for Mathematics and Physics.