Akiyama, Takahiro; Kasai, Hironori; Shibata, Yoshihiro; Tsutsumi, Masayoshi On a resolvent estimate of a system of Laplace operators with perfect wall condition. (English) Zbl 1114.35062 Funkc. Ekvacioj, Ser. Int. 47, No. 3, 361-394 (2004). Summary: This paper is concerned with the study of the system of Laplace operators with perfect wall condition in the \(L_p\) framework. 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 \(L_p\) framework. Cited in 7 Documents MSC: 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35J25 Boundary value problems for second-order elliptic equations 35P15 Estimates of eigenvalues in context of PDEs Keywords:system of Laplace operators; perfect wall condition; resolvent estimate PDFBibTeX XMLCite \textit{T. Akiyama} et al., Funkc. Ekvacioj, Ser. Int. 47, No. 3, 361--394 (2004; Zbl 1114.35062) Full Text: DOI