Boundary Value Problems
Volume 2007 (2007), Article ID 35825, 28 pages
doi:10.1155/2007/35825
Research Article
Interior Gradient Estimates for Nonuniformly Parabolic Equations II
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.
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.