Quadrature Domains for the Helmholtz Equation with Applications to Non-scattering Phenomena
Journal article, 2024
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.
Non-scattering phenomena
Metaharmonic functions
Acoustic equation
Quadrature domain
Partial balayage
Mean value theorem
Helmholtz equation
Author
Pu Zhao Kow
University of Jyväskylä
Simon Larson
Chalmers, Mathematical Sciences, Analysis and Probability Theory
Mikko Salo
University of Jyväskylä
Henrik Shahgholian
Royal Institute of Technology (KTH)
Potential Analysis
0926-2601 (ISSN) 1572-929X (eISSN)
Vol. 60 1 387-424Subject Categories (SSIF 2011)
Algebra and Logic
Computational Mathematics
Mathematical Analysis
DOI
10.1007/s11118-022-10054-5