Free boundary methods and non-scattering phenomena
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
Published inResearch in the Mathematical Sciences
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© The Author(s) 2021.
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.
PublisherSpringer Science and Business Media LLC
Publication in research information system
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Related funder(s)European Commission; Academy of Finland
Funding program(s)Centre of Excellence, AoF; Academy Project, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingM. 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.
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