Liouville theorems for a family of very degenerate elliptic non linear operators

2017/05/15 by Birindelli, Isabeau, Galise, Giulio, Leoni, Fabiana · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.05346

Abstract

We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators \cal P^±_k, defined respectively as the sum of the largest and the smallest k eigenvalues of the Hessian matrix. For the operator \cal P⁺_k we obtain results analogous to those which hold for the Laplace operator in space dimension k. Whereas, owing to the stronger degeneracy of the operator \cal P^-_k, we get totally different results.

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