July  2010, 28(3): 1069-1081. doi: 10.3934/dcds.2010.28.1069

Hölder continuity for integro-differential parabolic equations with polynomial growth respect to the gradient

1. 

Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637

Received  March 2010 Revised  April 2010 Published  April 2010

We prove that the solution to a parabolic integro-differential equation with a gradient dependence that satisfies a critical power growth becomes immediately Hölder continuous. We also obtain some results in the supercritical case.
Citation: Luis Silvestre. Hölder continuity for integro-differential parabolic equations with polynomial growth respect to the gradient. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 1069-1081. doi: 10.3934/dcds.2010.28.1069
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