This article is part of the series Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations.

Open Access Research Article

Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Gary M Lieberman

Author Affiliations

Department of Mathematics, Iowa State University, Ames, IA 50011, USA

Boundary Value Problems 2007, 2007:035825 doi:10.1155/2007/35825


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/035825


Received:31 May 2006
Revisions received:6 November 2006
Accepted:9 November 2006
Published:4 January 2007

© 2007 Lieberman

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previous methods. In particular, we have no restrictions on the maximum eigenvalue of the coefficient matrix and we obtain interior gradient estimates for so-called false mean curvature equation.

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