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Displaying similar documents to “Fully nonlinear second order elliptic equations : recent development”

On a comparison principle for a quasilinear elliptic boundary value problem of a nonmonotone type

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.

On some elliptic boundary-value problems with discontinuous nonlinearities

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.

Fully nonlinear second order elliptic equations with large zeroth order coefficient

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 C 2 , α -norm of the solution cannot lie in a certain interval of the positive real axis.