A Neumann eigenvalue problem for fully nonlinear operators

Abstract: In this paper we study the asymptotic behavior of the principal eigenvalues associated to the Pucci operator in bounded domain $\Omega$ with Neumann/Robin boundary condition i.e. $\partial_n u=\alpha u$ when $\alpha$ tends to infinity. This study requires Lipschitz estimates up to the boundary that are interesting in their own rights.