A local compactness theorem for Maxwell's equations
A local compactness theorem for Maxwell's equations
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DOI：
10.1002/mma.1670020103
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发表时间：
1980
影响因子：
2.9
通讯作者：
C. Weber;P. Werner
中科院分区：
文献类型：
--
作者：
C. Weber;P. Werner
本文给出了一个证明，有效的一大类有界域，以下紧性声明：设G是有界区域，β是G上满足一定限制的张量值函数，{n}是G上的向量值函数序列，其中{n}，{curl n}和{div（β n）}的L2-范数有界，且当n在G的边界上满足xn = 0或（β Fn）= 0时，{n}有L2收敛子列.第一个边界条件由电场满足，第二个边界条件由磁场在理想导电边界处满足，如果β分别被解释为电介电常数ε或磁导率μ。这些紧性陈述是必不可少的应用抽象散射理论的边值问题的麦克斯韦方程。
The paper gives a proof, valid for a large class of bounded domains, of the following compactness statements: Let G be a bounded domain, β be a tensor-valued function on G satisfying certain restrictions, and let {n} be a sequence of vector-valued functions on G where the L2-norms of {n}, {curl n}, and {div(β n)} are bounded, and where all n either satisfy x n = 0 or (β Fn) = 0 at the boundary ∂G of G ( = normal to ∂G): then {n} has a L2-convergent subsequence. The first boundary condition is satisfied by electric fields, the second one by magnetic fields at a perfectly conducting boundary ∂G if β is interpreted as electric dielectricity ϵ or as magnetic permeability μ, respectively. These compactness statements are essential for the application of abstract scattering theory to the boundary value problem for Maxwell's equations.