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arXiv:2204.13934 [math.AP]AbstractReferencesReviewsResources

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

Pu-Zhao Kow, Simon Larson, Mikko Salo, Henrik Shahgholian

Published 2022-04-29Version 1

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.

Comments: 42 pages, 6 figures
Categories: math.AP
Subjects: 35J05, 35J15, 35J20, 35R30, 35R35
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