Limits of solutions of p-Laplace equations as p goes to infinity and related variational problems

Hitoshi Ishii, Paola Loreti

    研究成果: Article査読

    14 被引用数 (Scopus)

    抄録

    We show that the convergence, as p → ∞, of the solution u p of the Dirichlet problem for -Δpu(x) = f(x) in a bounded domain ω ⊂ Rn with zero-Dirichlet boundary condition and with continuous f in the following cases: (i) one-dimensional case, radial cases; (ii) the case of no balanced family; and (iii) two cases with vanishing integral. We also give some properties of the maximizers for the functional ∫ω f(x)v(x) dx in the space of functions v ∈ C(ω̄) ∩ W1,∞(ω) satisfying v| ∂ω =0 and ||Dv||L∞(ω) ≤1.

    本文言語English
    ページ(範囲)411-437
    ページ数27
    ジャーナルSIAM Journal on Mathematical Analysis
    37
    2
    DOI
    出版ステータスPublished - 2006

    ASJC Scopus subject areas

    • 数学 (全般)
    • 分析
    • 応用数学
    • 数値解析

    フィンガープリント

    「Limits of solutions of p-Laplace equations as p goes to infinity and related variational problems」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

    引用スタイル