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

^*この研究の対応する著者

研究成果: Article › 査読

30 被引用数 (Scopus)

抄録

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.

本文言語	English
ジャーナル	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
DOI	https://doi.org/10.1016/j.anihpc.2017.05.003
出版ステータス	Accepted/In press - 2017 1月 7

ASJC Scopus subject areas

分析
数理物理学

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10.1016/j.anihpc.2017.05.003

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T2 - Maximum principle and its consequences

AU - Birindelli, Isabeau

AU - Galise, Giulio

AU - Ishii, Hitoshi

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Y1 - 2017/1/7

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

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

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