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 Jan 1

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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