Displaying similar documents to “New a priori estimates for q -nonlinear elliptic systems with strong nonlinearities in the gradient, 1 < q < 2 .”

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.

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.

Estimates on elliptic equations that hold only where the gradient is large

Cyril Imbert, Luis Silvestre (2016)

Journal of the European Mathematical Society

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We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.

Nonzero and positive solutions of a superlinear elliptic system

Mario Zuluaga Uribe (2001)

Archivum Mathematicum

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In this paper we consider the existence of nonzero solutions of an undecoupling elliptic system with zero Dirichlet condition. We use Leray-Schauder Degree Theory and arguments of Measure Theory. We will show the existence of positive solutions and we give applications to biharmonic equations and the scalar case.