Singularities almost always scatter: Regularity results for non‐scattering inhomogeneities
Singularities almost always scatter: Regularity results for non‐scattering inhomogeneities
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奇点几乎总是散射：非散射不均匀性的规律性结果
DOI：
10.1002/cpa.22117
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发表时间：
2021
影响因子：
3
通讯作者：
Michael S. Vogelius
中科院分区：
文献类型：
--
作者：
F. Cakoni;Michael S. Vogelius
在本文中，我们检验了非均匀性是非散射的必要条件，或者等价地，通过否定，检验了非均匀性是非散射的充分条件。这些条件是根据非均匀性边界的规则性来表述的。我们从二维和三维两方面考察了大类入射波。我们的分析很大程度上受到了Williams的分析的影响，Williams的分析确立了一个不具有庞培属性的域具有真正的分析边界。这一分析，以及我们的分析，在很大程度上依赖于Kinderlehrer、Nirenberg和Caffarelli的经典自由边界正则性结果。
In this paper we examine necessary conditions for an inhomogeneity to be non‐scattering, or equivalently, by negation, sufficient conditions for it to be scattering. These conditions are formulated in terms of the regularity of the boundary of the inhomogeneity. We examine broad classes of incident waves in both two and three dimensions. Our analysis is greatly influenced by the analysis carried out by Williams in order to establish that a domain, which does not possess the Pompeiu Property, has a real analytic boundary. That analysis, as well as ours, relies crucially on classical free boundary regularity results due to Kinderlehrer and Nirenberg, and Caffarelli.
DOI：
10.1080/03605302.2020.1843489
发表时间：
2019-05
影响因子：
1.9
作者：
F. Cakoni;Jingni Xiao
通讯作者：
F. Cakoni;Jingni Xiao