Uniqueness sets for minimization formulas

Yasuhiro Fujita, Hitoshi Ishii

    Research output: Contribution to journalArticle

    Abstract

    In this paper, we consider minimization formulas which arise typically in optimal control and weak KAM theory for Hamilton Jacobi equations. Given a minimization formula, we define a uniqueness set for the formula, which replaces the original region of minimization without changing its values. Our goal is to provide a necessary and sufficient condition that a given set be a uniqueness set. We also provide a characterization of the existence of a minimal uniqueness set with respect to set inclusion.

    Original languageEnglish
    Pages (from-to)579-588
    Number of pages10
    JournalDifferential and Integral Equations
    Volume25
    Issue number5-6
    Publication statusPublished - 2012 May

    Fingerprint

    Uniqueness
    KAM Theory
    Hamilton-Jacobi Equation
    Optimal Control
    Inclusion
    Necessary Conditions
    Sufficient Conditions

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Fujita, Y., & Ishii, H. (2012). Uniqueness sets for minimization formulas. Differential and Integral Equations, 25(5-6), 579-588.

    Uniqueness sets for minimization formulas. / Fujita, Yasuhiro; Ishii, Hitoshi.

    In: Differential and Integral Equations, Vol. 25, No. 5-6, 05.2012, p. 579-588.

    Research output: Contribution to journalArticle

    Fujita, Y & Ishii, H 2012, 'Uniqueness sets for minimization formulas', Differential and Integral Equations, vol. 25, no. 5-6, pp. 579-588.
    Fujita, Yasuhiro ; Ishii, Hitoshi. / Uniqueness sets for minimization formulas. In: Differential and Integral Equations. 2012 ; Vol. 25, No. 5-6. pp. 579-588.
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