Maximum Principles and Bounds in Some Inhomogeneous Elliptic Boundary Value Problems
- 1 October 1977
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 8 (5) , 871-878
- https://doi.org/10.1137/0508066
Abstract
A class of inhomogeneous nonlinear elliptic boundary value problems is considered. The Hopf maximum principles are used to deduce that certain functionals defined for solutions of the problem attain a maximum at a critical point of the solution. These maximum principles are then used to determine bounds for quantities of interest in some physical problems.Keywords
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