Global Compensated Compactness Theorem for General Differential Operators of First Order

Hideo Kozono, Taku Yanagisawa

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    Let A1(x, D) and A2(x, D) be differential operators of the first order acting on l-vector functions u = (u1, . . . , u1) in a bounded domain Ω ⊂ ℝn with the smooth boundary ∂Ω. We assume that the H1-norm, is equivalent to, where Bi = Bi(x, ν) is the trace operator onto ∂ Ω associated with Ai(x, D) for i = 1, 2 which is determined by the Stokes integral formula (ν: unit outer normal to ∂Ω. Furthermore, we impose on A1 and A2 a cancellation property such as A1A2′ = 0 and A2A1′ = 0, where Ai′ is the formal adjoint differential operator of Ai(i = 1, 2). Suppose that and converge to u and v weakly in L2(Ω), respectively. Assume also that and are bounded in L2(Ω). If either or is bounded in H1/2(∂Ω), then it holds that. We also discuss a corresponding result on compact Riemannian manifolds with boundary.

    Original languageEnglish
    Pages (from-to)879-905
    Number of pages27
    JournalArchive for Rational Mechanics and Analysis
    Volume207
    Issue number3
    DOIs
    Publication statusPublished - 2013

    Fingerprint

    Compensated Compactness
    Differential operator
    First-order
    Adjoint Operator
    Manifolds with Boundary
    Integral Formula
    Cancellation
    Stokes
    Theorem
    Compact Manifold
    Riemannian Manifold
    Bounded Domain
    Trace
    Converge
    Norm
    Unit
    Operator

    ASJC Scopus subject areas

    • Analysis
    • Mechanical Engineering
    • Mathematics (miscellaneous)

    Cite this

    Global Compensated Compactness Theorem for General Differential Operators of First Order. / Kozono, Hideo; Yanagisawa, Taku.

    In: Archive for Rational Mechanics and Analysis, Vol. 207, No. 3, 2013, p. 879-905.

    Research output: Contribution to journalArticle

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