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arXiv · 2204.13934

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

Pu-Zhao Kow·Simon Larson·Mikko Salo·Henrik Shahgholian
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Abstract

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.

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Pu-Zhao Kow, Simon Larson, Mikko Salo, Henrik Shahgholian. 2022-04-29. Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena. https://doi.org/10.1007/s11118-022-10054-5

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