Boundary Value Problems
Volume 2007 (2007), Article ID 35825, 28 pages
Research Article

Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Gary M. Lieberman

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

Received 31 May 2006; Revised 6 November 2006; Accepted 9 November 2006

Academic Editor: Vincenzo Vespri

Copyright © 2007 Gary M. 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.