In this paper we investigate the validity and the consequences of the maximum principle for degenerate elliptic operators whose higher order term is the sum of k eigenvalues of the Hessian. In particular we shed some light on some very unusual phenomena due to the degeneracy of the operator. We prove moreover Lipschitz regularity results and boundary estimates under convexity assumptions on the domain. As a consequence we obtain the existence of solutions of the Dirichlet problem and of principal eigenfunctions.
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|Publication status||Accepted/In press - 2017 Jan 7|
- Eigenvalue problem
- Fully nonlinear degenerate elliptic PDE
- Maximum principle
ASJC Scopus subject areas
- Mathematical Physics