Maxwell's Equations and Dielectric Obstacles with Lipschitz Boundaries
Maxwell's Equations and Dielectric Obstacles with Lipschitz Boundaries
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DOI：
10.1112/s0024610798005900
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发表时间：
1998-02
期刊：
影响因子：
--
通讯作者：
R. Torres
中科院分区：
文献类型：
--
作者：
R. Torres
用层势法求解了介质目标对时间谐波电磁波的经典传输问题。仅假定对象的表面是Lipschitz流形。与光滑表面的情况不同，伪微分算子的演算和某些边界算子的紧致性都不是可用的工具。然而，本文所使用的解的特殊表示和边界数据空间的选择使得问题可以通过非光滑区域上的椭圆型偏微分方程组的调和分析技术来处理。
The classical transmission problem for the scattering of time‐harmonic electromagnetic waves by a dielectric object is solved using layer potential techniques. The surface of the object is only assumed to be a Lipschitz manifold. Unlike in the case of smoother surfaces, neither the calculus of pseudodifferential operators nor the compactness of certain boundary operators are available tools. Nevertheless, the particular representation of the solutions and the choice of the space of boundary data used in the paper make the problem tractable via harmonic analysis techniques for elliptical partial differential equations in nonsmooth domains.