On a Resolvent Estimate of a System of Laplace Operators with Perfect Wall Condition

T. Akiyama, Y. Shibata, M. Tsutsumi, H. Kasai

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

This paper is concerned with the study of the system of Laplace operators with perfect wall condition in the Lpframework. Our study includes a bounded domain, an exterior domain and a domain having noncompact boundary such as a perturbed half space. A direct application of our study is to prove the analyticity of the semigroup corresponding to the Maxwell equation of parabolic type, which appears as a linearized equation in the study of the nonstationary problem concerning the Ginzburg-Landau-Maxwell equation describing the Ginzburg-Landau model for superconductivity, the magnetohydrodynamic equation and the Navier-Stokes equation with Neumann boundary condition. And also, our theory is applicable to some solvability of the stationary problem of these nonlinear equations in the Lpframework.

Original languageEnglish
Pages (from-to)361-394
Number of pages34
JournalFunkcialaj Ekvacioj
Volume47
Issue number3
DOIs
Publication statusPublished - 2004 Jan 1

Keywords

  • A system of Laplace operators
  • Perfect wall condition
  • Resolvent estimate

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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