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Michal Křížek, Liping Liu (1996)
Applicationes Mathematicae
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A nonlinear elliptic partial differential equation with the Newton boundary conditions is examined. We prove that for greater data we get a greater weak solution. This is the so-called comparison principle. It is applied to a steady-state heat conduction problem in anisotropic magnetic cores of large transformers.
Nicolai V. Krylov (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Uraltseva, N. N.
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Edward N. Dancer, Shusen Yan (2007)
Bollettino dell'Unione Matematica Italiana
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We show how a change of variable and peak solution methods can be used to prove that a number of nonlinear elliptic partial differential equations have many solutions.
Alexander Zenisek (1987)
Numerische Mathematik
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Danet, Cristian-Paul (2005)
Journal of Applied Mathematics
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Guy Barles, Alain-Philippe Blanc, Christine Georgelin, Magdalena Kobylanski (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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L. C. Evans, Pierre-Louis Lions (1981)
Annales de l'institut Fourier
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We prove the existence of classical solutions to certain fully non-linear second order elliptic equations with large zeroth order coefficient. The principal tool is an estimate asserting that the -norm of the solution cannot lie in a certain interval of the positive real axis.
Mohammad Mujalli Al-Mahameed (2005)
Archivum Mathematicum
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We introduce weak discrete maximum principles for matrix equations associated with some elliptic problems. We also give an example on discrete maximum principles.