A family of degenerate elliptic operators: Maximum principle and its consequences

Isabeau Birindelli; Giulio Galise; Hitoshi Ishii

doi:10.1016/j.anihpc.2017.05.003

A family of degenerate elliptic operators: Maximum principle and its consequences

Isabeau Birindelli, Giulio Galise, Hitoshi Ishii

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24 Citations (Scopus)

Abstract

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.

Original language	English
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
DOIs	https://doi.org/10.1016/j.anihpc.2017.05.003
Publication status	Accepted/In press - 2017 Jan 7

Keywords

Eigenvalue problem
Fully nonlinear degenerate elliptic PDE
Maximum principle

ASJC Scopus subject areas

Analysis
Mathematical Physics

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AU - Galise, Giulio

AU - Ishii, Hitoshi

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N2 - 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.

AB - 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.

KW - Eigenvalue problem

KW - Fully nonlinear degenerate elliptic PDE

KW - Maximum principle

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JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

ER -

A family of degenerate elliptic operators: Maximum principle and its consequences

Abstract

Keywords

ASJC Scopus subject areas

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