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On a resolvent estimate of a system of Laplace operators with perfect wall condition. (English) Zbl 1114.35062

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.

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
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