Relaxation of Hamilton-Jacobi Equations

Hitoshi Ishii*, Paola Loreti

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)


    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
    Issue number4
    Publication statusPublished - 2003 Oct

    ASJC Scopus subject areas

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


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