The Neumann problem for singular fully nonlinear operators

Abstract

We consider the Neumann problem in $C^2$ bounded domains for fully nonlinear second order operators which are elliptic, homogenous with lower order terms. Inspired by \cite{bnv}, we define the concept of principal eigenvalue and we characterize it through the maximum principle. Moreover, Lipschitz regularity, uniqueness and existence results for solutions of the Neumann problem are given.

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• The principal eigenvalue of the $\infty$-Laplacian with the Neumann boundary condition