奇点几乎总是散射的:非散射非均匀性的规则性结果

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-07-17 DOI:10.1002/cpa.22117

Fioralba Cakoni, Michael S. Vogelius

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引用次数: 16

摘要

在本文中，我们研究了不均匀性是非散射的必要条件，或者等价地，通过否定，它是散射的充分条件。这些条件是根据不均匀性边界的规律性来表述的。我们研究了二维和三维的各种入射波。我们的分析在很大程度上受到了威廉姆斯的分析的影响，威廉姆斯的分析是为了确定一个不具有庞贝属性的领域有一个真正的分析边界。这种分析，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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Singularities almost always scatter: Regularity results for non-scattering inhomogeneities

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.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.