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

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.

45 pages, 6 figures

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