Boundary Value Problems
Volume 2006 (2006), Article ID 64543, 13 pages
doi:10.1155/BVP/2006/64543
Maximum principles for a class of nonlinear second-order elliptic
boundary value problems in divergence form
Department of Mathematics and Computer Science, Ovidius University, Constanta 900 527, Romania
Received 22 January 2006; Accepted 26 March 2006
Copyright © 2006 Cristian Enache. 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
For a class of nonlinear elliptic boundary value problems in
divergence form, we construct some general elliptic inequalities
for appropriate combinations of u(x) and |∇u|2, where u(x) are the solutions of our problems.
From these inequalities, we derive, using Hopf's maximum
principles, some maximum principles for the appropriate
combinations of u(x) and |∇u|2, and we list
a few examples of problems to which these maximum principles may
be applied.