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.
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