Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions

David Arcoya, Colette De Coster, Louis Jeanjean, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    In this note we present some uniqueness and comparison results for a class of problem of the form. (0.1)-Lu=H(x,u,∇;u)+h(x),u∈H01(Ω)∩L∞(Ω), where Ω⊂RN, N≥. 2 is a bounded domain, L is a general elliptic second order linear operator with bounded coefficients and H is allowed to have a critical growth in the gradient. In some cases our assumptions prove to be sharp.

    Original languageEnglish
    Pages (from-to)772-780
    Number of pages9
    JournalJournal of Mathematical Analysis and Applications
    Volume420
    Issue number1
    DOIs
    Publication statusPublished - 2014 Dec 1

    Fingerprint

    Critical Growth
    Quasilinear Elliptic Equation
    Comparison Result
    Growth Conditions
    Linear Operator
    Bounded Domain
    Uniqueness
    Gradient
    Coefficient
    Class
    Form

    Keywords

    • Quadratic growth in the gradient
    • Quasilinear elliptic equations
    • Uniqueness of solution

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions. / Arcoya, David; De Coster, Colette; Jeanjean, Louis; Tanaka, Kazunaga.

    In: Journal of Mathematical Analysis and Applications, Vol. 420, No. 1, 01.12.2014, p. 772-780.

    Research output: Contribution to journalArticle

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