三维常折射率球不均匀体的散射场
On the scattered field generated by a ball inhomogeneity of constant index in dimension three
摘要：
我们考虑标量亥姆霍兹方程的解，其中势（或指数）取两个正值，一个在半径为$\eps$的球内，另一个在球外。在这篇短文中，我们报告最近在[1]中在二维情况下得到的结果可以很容易地推广到三维。特别是，我们提供了尖锐的估计，由这个球的不均匀性所造成的散射场的大小，任何频率和任何对比度。我们还提供了宽带估计，即对于任何对比度以及在使用$\eps$趋于零的集合之外的任何频率，散射场的统一界限。
英文摘要：
We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a ball of radius $\eps$ and another one outside. In this short paper, we report that the results recently obtained in the two dimensional case in [1] can be easily extended to three dimensions. In particular, we provide sharp estimates of the size of the scattered field caused by this ball inhomogeneity, for any frequencies and any contrast. We also provide a broadband estimate, that is, a uniform bound for the scattered field for any contrast, and any frequencies outside of a set which tends to zero with $\eps$.
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。
