2016/12/06 by Isabeau Birindelli, Birindelli, Isabeau, Giulio Galise +3 · 1 citation
Computer Science · Mathematics · #35J60 #35J70 #49L25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1612.01700
openalex publication_date 2016/12/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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 for problems in convex domains which are intersections of ball of same radius. We prove also that smooth bounded strictly convex domains are part of this class. As a consequence we obtain the existence of solutions of the Dirichlet problem and of principal eigenfunctions.