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

Mathematics – Analysis of PDEs

Scientific paper

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30 pages, 1 figure

Scientific paper

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.

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