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
收藏
页码：387 / 424
页数：38
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