Representation formulas for solutions of Hamilton-Jacobi equations with convex hamiltonians

Hitoshi Ishii, Hiroyoshi Mitake

    Research output: Contribution to journalArticle

    30 Citations (Scopus)

    Abstract

    We establish general representation formulas for solutions of Hamilton-Jacobi equations widi convex Hamiltonians. In order to treat representation formulas on general domains, we introduce a notion of ideal boundary similar to the Martin boundary [21] in potential theory. We apply such representation formulas to investigate maximal solutions, in certain classes of functions, of Hamilton-Jacobi equations. Part of the results in this paper has been announced in [22]. Indiana University Mathematics Journal

    Original languageEnglish
    Pages (from-to)2159-2183
    Number of pages25
    JournalIndiana University Mathematics Journal
    Volume56
    Issue number5
    DOIs
    Publication statusPublished - 2007

    Keywords

    • Aubry sets
    • Hamilton-Jacobi equations
    • Representation fotmula
    • State constraint problem
    • Weak KAM theory

    ASJC Scopus subject areas

    • Mathematics(all)

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