Displaying similar documents to “Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions”

Uniqueness of solutions for some elliptic equations with a quadratic gradient term

David Arcoya, Sergio Segura de León (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study a comparison principle and uniqueness of positive solutions for the homogeneous Dirichlet boundary value problem associated to quasi-linear elliptic equations with lower order terms. A model example is given by - Δ u + λ | ∇ u | 2 u r = f ( x ) , λ , r > 0 . The main feature of these equations consists in having a quadratic gradient term in which singularities are allowed. The arguments employed here also work to deal with equations having lack of ellipticity...

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.

Absorption effects for some elliptic equations with singularities

A. Porretta (2005)

Bollettino dell'Unione Matematica Italiana

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We give an expository review of recent results obtained for elliptic equations having natural growth terms of absorption type and singular data. As a new result, we provide an application to the case of lower order terms of subcritical growth, proving a general solvability result with measure data for a class of equations modeled on (1.6).