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Interior Gradient Estimates for Nonuniformly Parabolic Equations II

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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Correspondence to Gary M Lieberman.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Lieberman, G.M. Interior Gradient Estimates for Nonuniformly Parabolic Equations II. Bound Value Probl 2007, 035825 (2007). https://doi.org/10.1155/2007/35825

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Large Class