Regularity and uniqueness of the first eigenfunction for singular fully non linear operators

Isabeau Birindelli, Francoise Demengel

Published 2009-09-21Version 1

In this article we prove that solutions of singular fully nonlinear partial differential equations are $C^{1,\beta}$. We also prove the simplicity of the principal eigenvalues for the Dirichlet Problem associated to these operators using that regularity, a strict comparison principle and Sard's theorem.