**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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