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 | |
| Publication status | Accepted/In press - 2017 Jan 7 |
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Keywords
- Eigenvalue problem
- Fully nonlinear degenerate elliptic PDE
- Maximum principle
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
Cite this
A family of degenerate elliptic operators : Maximum principle and its consequences. / Birindelli, Isabeau; Galise, Giulio; Ishii, Hitoshi.
In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 07.01.2017.Research output: Contribution to journal › Article
}
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 -