Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions

Guy Barles; Alain-Philippe Blanc; Christine Georgelin; Magdalena Kobylanski

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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 $- Δ u + λ \frac{{| \nabla u |}^{2}}{u^{r}} = f (x), λ, r > 0 .$ 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...

Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations.

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Yu Yuan (2001)

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B. H. Gilding (1989)

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Fully nonlinear second order elliptic equations with large zeroth order coefficient

L. C. Evans, Pierre-Louis Lions (1981)

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