Geometric PDE and Applied Analysis Seminar (January 23, 2024)

Title: Robust near-diagonal Green function estimates

Speaker: Prof. Minhyun Kim (Hanyang University)

Abstract: In this talk I would like to discuss sharp near-diagonal pointwise bounds for the Green function for nonlocal operators of fractional order. The novelty of our results it two-fold: the estimates are robust as the order of operators approaches 2 and we prove the bounds without making use of the Dirichlet heat kernel. In this way we can cover cases, in which the Green function satisfies isotropic bounds but the heat kernel does not. This talk is based on a joint work with Moritz Kassmann and Ki-Ahm Lee.