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Maximum principles for a class of nonlinear second-order elliptic boundary value problems in divergence form

Abstract

For a class of nonlinear elliptic boundary value problems in divergence form, we construct some general elliptic inequalities for appropriate combinations of and, where are the solutions of our problems. From these inequalities, we derive, using Hopf's maximum principles, some maximum principles for the appropriate combinations of and, and we list a few examples of problems to which these maximum principles may be applied.

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Correspondence to Cristian Enache.

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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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Enache, C. Maximum principles for a class of nonlinear second-order elliptic boundary value problems in divergence form. Bound Value Probl 2006, 64543 (2006). https://doi.org/10.1155/BVP/2006/64543

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Maximum Principle