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

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.

24 pages

References in corpus (2)

• Nonlinear Eigenvalues and Bifurcation Problems for Pucci's Operator
• The Dirichlet problem for singular fully nonlinear operators

Cited by in corpus (5)

• $C^{1,\alpha }$ regularity of solutions of degenerate fully non-linear elliptic equations
• Some remarks on singular solutions of nonlinear elliptic equations. III: viscosity solutions, including parabolic operators
• ABP and global Holder estimates for fully nonlinear elliptic equations in unbounded domains
• On viscosity solutions of space-fractional diffusion equations of Caputo type
• Optimal C^{1,\apha} regularity for degenerate fully nonlinear elliptic equations with Neumann boundary condition