MR2126323 Akiyama, T., Kasai, H., Shibata, Y. and Tsutsumi, M. T. AKIYAMA, H. KASAI, Y. SHIBATA and M. TSUTSUMI On a Resolvent Estimate of a System of Laplace Operators with Perfect Wall Condition Funkcialaj Ekvacioj. Serio Internacia 47 2004 361--394 http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-3/47_361.pdf http://www.ams.org/mathscinet-getitem?mr=MR2126323 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. A system of Laplace operators, Perfect wall condition, Resolvent estimate. 35J55, 35J25. 47-361 2004 On a Resolvent Estimate of a System of Laplace Operators with Perfect Wall Condition AKIYAMA, T., KASAI, H., SHIBATA, Y. and TSUTSUMI, M. T. AKIYAMA, H. KASAI, Y. SHIBATA and M. TSUTSUMI
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