A family of degenerate elliptic operators

Maximum principle and its consequences

Isabeau Birindelli, Giulio Galise, Hitoshi Ishii

    Research output: Contribution to journal › Article

    4 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 languageEnglish
    JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
    DOIs
    Publication statusAccepted/In press - 2017 Jan 7

    Fingerprint

    Degenerate Elliptic Operators
    Maximum principle
    Maximum Principle
    Degeneracy
    Eigenvalues and eigenfunctions
    Dirichlet Problem
    Eigenfunctions
    Lipschitz
    Convexity
    Existence of Solutions
    Regularity
    Higher Order
    Eigenvalue
    Term
    Operator
    Estimate
    Family

    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

    Birindelli, I, Galise, G & Ishii, H 2017, 'A family of degenerate elliptic operators: Maximum principle and its consequences', Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. https://doi.org/10.1016/j.anihpc.2017.05.003
    Birindelli I, Galise G, Ishii H. A family of degenerate elliptic operators: Maximum principle and its consequences. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 2017 Jan 7. https://doi.org/10.1016/j.anihpc.2017.05.003
    Birindelli, Isabeau ; Galise, Giulio ; Ishii, Hitoshi. / A family of degenerate elliptic operators : Maximum principle and its consequences. In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 2017.
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