Nonlinear oblique boundary value problems for Hessian equations in two dimensions

John Urbas

    Research output: Contribution to journalArticlepeer-review

    40 Citations (Scopus)

    Abstract

    We study nonlinear oblique boundary value problems for nonuniformly elliptic Hessian equations in two dimensions. These are equations whose principal part is given by a suitable symmetric function of the eigenvalues of the Hessian matrix D2u of the solution u. An interesting feature of our second derivative estimates is the need for certain strong structural hypotheses on the boundary condition, which are not needed in the uniformly elliptic case. Restrictions of this type are natural in our context; we present examples showing that second derivative bounds may fail if we do not assume such conditions.

    Original languageEnglish
    Pages (from-to)507-575
    Number of pages69
    JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
    Volume12
    Issue number5
    DOIs
    Publication statusPublished - 1 Sept 1995

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