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Open Access Open Badges 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

Published: 4 January 2007


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.