Fully nonlinear second order elliptic equations : recent development

Nicolai V. Krylov

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

On fully nonlinear elliptic equations of second order

L. Nirenberg (1988-1989)

Séminaire Équations aux dérivées partielles (Polytechnique)

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New a priori estimates for $q$ -nonlinear elliptic systems with strong nonlinearities in the gradient, $1 < q < 2$ .

Arkhipova, A.A. (2004)

Journal of Mathematical Sciences (New York)

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Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations

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.

Oblique boundary value problems for nonlinear parabolic equations

Uraltseva, N. N.

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Nonexistence of classical solutions of the Dirichlet problem for fully nonlinear elliptic equations

N. Kutev (1991)

Archivum Mathematicum

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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.

𝒞1,β regularity for Dirichlet problems associated to fully nonlinear degenerate elliptic equations

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.