Free boundary methods and non-scattering phenomena
Abstract
We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave. At zero frequency, we use quadrature domains to show that there are also obstacles with inward cusps having this property. In the converse direction, under a nonvanishing condition for the incident wave, we show that there is a dichotomy for boundary points of any penetrable obstacle having this property: either the boundary is regular, or the complement of the obstacle has to be very thin near the point. These facts are proved by invoking results from the theory of free boundary problems.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Springer Science and Business Media LLC
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202110215320Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
2522-0144
DOI
https://doi.org/10.1007/s40687-021-00294-z
Language
English
Published in
Research in the Mathematical Sciences
Citation
- Salo, M., & Shahgholian, H. (2021). Free boundary methods and non-scattering phenomena. Research in the Mathematical Sciences, 8(4), Article 58. https://doi.org/10.1007/s40687-021-00294-z
License
Funder(s)
European Commission
Research Council of Finland
Research Council of Finland
Funding program(s)
ERC Consolidator Grant
Centre of Excellence, AoF
Academy Project, AoF
ERC Consolidator Grant
Huippuyksikkörahoitus, SA
Akatemiahanke, SA
Additional information about funding
M. S. was supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Modelling and Imaging, Grant Numbers 312121 and 309963) and by the European Research Council under Horizon 2020 (ERC CoG 770924). H. Sh. was supported in part by Swedish Research Council.
Copyright© The Author(s) 2021.