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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

31 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

Access to Document

10.1016/j.anihpc.2017.05.003

Cite this

@article{715b8ff524a347f0aca3bc33d774b357,

title = "A family of degenerate elliptic operators: Maximum principle and its consequences",

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.",

keywords = "Eigenvalue problem, Fully nonlinear degenerate elliptic PDE, Maximum principle",

author = "Isabeau Birindelli and Giulio Galise and Hitoshi Ishii",

year = "2017",

month = jan,

day = "7",

doi = "10.1016/j.anihpc.2017.05.003",

language = "English",

journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",

issn = "0294-1449",

publisher = "Elsevier Masson SAS",

}

TY - JOUR

T1 - A family of degenerate elliptic operators

T2 - Maximum principle and its consequences

AU - Birindelli, Isabeau

AU - Galise, Giulio

AU - Ishii, Hitoshi

PY - 2017/1/7

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

UR - http://www.scopus.com/inward/record.url?scp=85020201868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020201868&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2017.05.003

DO - 10.1016/j.anihpc.2017.05.003

M3 - Article

AN - SCOPUS:85020201868

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this