Quadrature Domains for the Helmholtz Equation with Applications to Non-scattering Phenomena

被引：5

作者：

Kow, Pu-Zhao ^{[1
]}

Larson, Simon ^{[2
,3
]}

Salo, Mikko ^{[1
]}

Shahgholian, Henrik ^{[4
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, Jyvaskyla 40014, Finland

[2] Chalmers Univ Technol, Math Sci, Gothenburg, Sweden

[3] Univ Gothenburg, SE-41296 Gothenburg, Sweden

[4] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

POTENTIAL ANALYSIS | 2024年 / 60卷 / 01期

关键词：

Quadrature domain; Non-scattering phenomena; Mean value theorem; Helmholtz equation; Acoustic equation; Metaharmonic functions; Partial balayage; OBSTACLE PROBLEM; CORNERS; BOUNDARY; REGULARITY;

D O I：

10.1007/s11118-022-10054-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We also give an application to inverse scattering problems, and show that there are non-scattering domains for the Helmholtz equation at any positive frequency that have inward cusps.

引用

页码：387 / 424

页数：38

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