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arXiv · 1705.05346

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

Isabeau Birindelli·Giulio Galise·Fabiana Leoni
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Abstract

We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators ${\cal P}^\pm_k$, 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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Isabeau Birindelli, Giulio Galise, Fabiana Leoni. 2017-05-15. Liouville theorems for a family of very degenerate elliptic non linear operators. https://arxiv.org/abs/1705.05346

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