Relaxation of Hamilton-Jacobi Equations

Hitoshi Ishii, Paola Loreti

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    We study the relaxation of Hamilton-Jacobi equations. The relaxation in our terminology is the following phenomenon: the pointwise supremum over a certain collection of subsolutions, in the almost everywhere sense, of a Hamilton-Jacobi equation yields a viscosity solution of the "convexified" Hamilton-Jacobi equation. This phenomenon has recently been observed in [13] in eikonal equations. We show in this paper that this relaxation is a common phenomenon for a wide range of Hamilton-Jacobi equations.

    Original languageEnglish
    Pages (from-to)265-304
    Number of pages40
    JournalArchive for Rational Mechanics and Analysis
    Volume169
    Issue number4
    DOIs
    Publication statusPublished - 2003 Oct

    Fingerprint

    Hamilton-Jacobi Equation
    Terminology
    Viscosity
    Eikonal Equation
    Subsolution
    Viscosity Solutions
    Supremum
    Range of data

    ASJC Scopus subject areas

    • Mechanics of Materials
    • Computational Mechanics
    • Mathematics(all)
    • Mathematics (miscellaneous)

    Cite this

    Relaxation of Hamilton-Jacobi Equations. / Ishii, Hitoshi; Loreti, Paola.

    In: Archive for Rational Mechanics and Analysis, Vol. 169, No. 4, 10.2003, p. 265-304.

    Research output: Contribution to journalArticle

    Ishii, Hitoshi ; Loreti, Paola. / Relaxation of Hamilton-Jacobi Equations. In: Archive for Rational Mechanics and Analysis. 2003 ; Vol. 169, No. 4. pp. 265-304.
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