Autumn School in Nonlinear Science 

07/10/2015, 11:00 — 12:00 — Abreu Faro Amphitheatre
Tuomo Kuusi, Aalto

Aspects of nonlocal regularity theory

Recently the fractional Laplacian operator $(−∆)^s$ and more general integro-differential operators with singular kernels of fractional differentiability of order $s \in (0,1)$ have been intensively studied.  After being investigated first from the perspective of potential theory and harmonic analysis, during the last decade also the regularity theory has obtained great interest. The aim of this minicourse is to go through some recent developments in the nonlocal regularity theory. The approach will be suitable also for many nonlinear problems.