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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Moritz Kassmann
University of Bielefeld
Title: Harnack inequality and Hölder regularity estimates for integro-differential operators

Abstract: In recent years, methods for differential operators of second order have been applied successfully to integro-differential operators of fractional order. In this context we concentrate on the Harnack inequality and Hölder regularity estimates. We show that one can formulate the Harnack inequality from 1887 in a way such that it holds for the Laplacian and fractional powers of the Laplacian at the same time. This generalizes to nonlocal Dirichlet forms. As a result, Hölder regularity estimates are obtained as a consequence of Harnack's inequality. We also discuss some counterexamples.

Date: Monday, February 28, 2011
Time: 3:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer