On fully nonlinear elliptic equations of second order
L. Nirenberg (1988-1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
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L. Nirenberg (1988-1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Arkhipova, A.A. (2004)
Journal of Mathematical Sciences (New York)
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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.
Uraltseva, N. N.
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N. Kutev (1991)
Archivum Mathematicum
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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.
Giovanni Anello (2005)
Annales Polonici Mathematici
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We establish two existence results for elliptic boundary-value problems with discontinuous nonlinearities. One of them concerns implicit elliptic equations of the form ψ(-Δu) = f(x,u). We emphasize that our assumptions permit the nonlinear term f to be discontinuous with respect to the second variable at each point.
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.
I. Birindelli, F. Demengel (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove Hölder regularity of the gradient, up to the boundary for solutions of some fully-nonlinear, degenerate elliptic equations, with degeneracy coming from the gradient.