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

Hitoshi Ishii, Paola Loreti

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)411-437
    Number of pages27
    JournalSIAM Journal on Mathematical Analysis
    Volume37
    Issue number2
    DOIs
    Publication statusPublished - 2006

    Keywords

    • ∞-Laplace equation
    • Asymptotic behavior
    • Eikonal equation
    • L variational problem
    • P-Laplace equation
    • Variational problem

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics
    • Numerical Analysis

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