6533b830fe1ef96bd12966d5

RESEARCH PRODUCT

Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena

Pu-zhao KowSimon LarsonMikko SaloHenrik Shahgholian

subject

metaharmonic functionsmatematiikkapartial balayageyhtälötmean value theoremMathematics::Numerical Analysis35J05 35J15 35J20 35R30 35R35quadrature domainnon-scattering phenomenaMathematics - Analysis of PDEsFOS: MathematicsHelmholtz equationacoustic equationAnalysisAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2022-01-01
10.1007/s11118-022-10054-5http://arxiv.org/abs/2204.13934