Riv. Mat. Univ. Parma, Vol. 5, No. 1, 2014

Moritz Kassmann [1] and Russell W. Schwab [2]

Regularity results for nonlocal parabolic equations

Pages: 183-212
Received: 14 May 2013   
Accepted in revised form: 8 August 2013
Mathematics Subject Classification (2010): Primary 35B65, Secondary 47G20, 60J75.

Keywords: Integro-differential operator, nonlocal operator, parabolic equation, Moser iteration, weak Harnack inequality, Hölder regularity.
Authors addresses:
[1] : Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
[2] : Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824, United States of America

Abstract: We survey recent regularity results for parabolic equations involving nonlocal operators like the fractional Laplacian. We extend the results of [28] and obtain regularity estimates for nonlocal operators with kernels not being absolutely continuous with respect to the Lebesgue measure.

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