Eigenvalue and Dirichlet problem for fully-nonlinear operators in non smooth domains

2008/03/26 by Isabeau Birindelli, Birindelli, I., Françoise Demengel +1 · 4 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0803.3739

Abstract

In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are similar to those of the p-Laplacian, the novelty resides in the fact that we consider the equations in bounded domains which only satisfy the exterior cone condition.

Cited by

• A quantitative Hopf-Oleinik lemma for degenerate fully nonlinear operators and applications to free boundary problems
• Harnack inequality for singular fully nonlinear operators and some existence results
• Some remarks on singular solutions of nonlinear elliptic equations. III:\n viscosity solutions, including parabolic operators
• Geometric gradient estimates for solutions to degenerate elliptic equations

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