Boundary Value Problems

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Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Boundary Value Problems20072007:035825

https://doi.org/10.1155/2007/35825

©  Gary M. Lieberman 2007

Received: 31 May 2006

Accepted: 9 November 2006

Published: 4 January 2007

Abstract

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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Authors’ Affiliations

(1)
Department of Mathematics, Iowa State University

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Copyright

© Gary M. Lieberman 2007

This article is published under license to BioMed Central Ltd. 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.