Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions

Hitoshi Ishii

    研究成果: Article査読

    13 被引用数 (Scopus)

    抄録

    We study convex Hamilton-Jacobi equations H(x,Du)=0 and ut+H(x,Du)=0 in a bounded domain Ω of Rn with the Neumann type boundary condition Dγu=g in the viewpoint of weak KAM theory, where γ is a vector field on the boundary ∂ Ω pointing a direction oblique to ∂ Ω We establish the stability under the formations of infimum and of convex combinations of subsolutions of convex Hamilton-Jacobi equations, some comparison and existence results for convex and coercive Hamilton-Jacobi equations with the Neumann type boundary condition as well as existence results for the Skorokhod problem. We define the Aubry set associated with the Neumann type boundary problem and establish some properties of the Aubry set including the existence results for the "calibrated" extremals for the corresponding action functional (or variational problem).

    本文言語English
    ページ(範囲)99-135
    ページ数37
    ジャーナルJournal des Mathematiques Pures et Appliquees
    95
    1
    DOI
    出版ステータスPublished - 2011 1

    ASJC Scopus subject areas

    • 応用数学
    • 数学 (全般)

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