非光滑外区域上的广义电磁静力学
Generalized Electro-Magneto Statics in Nonsmooth Exterior Domains
摘要：
我们发展了一个广义电磁静态Maxwell系统的解理论，该系统在一个具有各向异性系数的外部区域中以一定的速度收敛到无穷远。我们的主要目标是处理一些多项式加权的索伯列夫空间的右侧数据，并获得解决方案，这是一个有限的特殊广义球谐函数在另一个适当加权的索伯列夫空间的总和。作为一个副产品，我们证明了广义球谐展开适合麦克斯韦方程组。特别是，我们的解决方案理论将使我们能够给一个特殊的静态解决方案运营商的更高的权力的意义。最后，我们展示了如何将这种加权静态解理论扩展到处理非均匀边界数据。本文是三篇完整揭示时谐麦克斯韦方程组解的低频行为的系列论文中的第二篇。
英文摘要：
We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand side data from some polynomially weighted Sobolev spaces and obtain solutions which are up to a finite sum of special generalized spherical harmonics in another appropriately weighted Sobolev space. As a byproduct we prove a generalized spherical harmonics expansion suited for Maxwell equations. In particular, our solution theory will allow us to give meaning to higher powers of a special static solution operator. Finally we show, how this weighted static solution theory can be extended to handle inhomogeneous boundary data as well. This paper is the second one in a series of three papers, which will completely reveal the low frequency behavior of solutions of the time-harmonic Maxwell equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
