On Positivity Sets for Helmholtz Solutions
Abstract
We address the question of finding global solutions of the Helmholtz equation that are positive in a given set. This question arises in inverse scattering for penetrable obstacles. In particular, we show that there are solutions that are positive on the boundary of a bounded Lipschitz domain.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202309074970Use this for linking
Review status
Peer reviewed
ISSN
2305-221X
DOI
https://doi.org/10.1007/s10013-023-00646-y
Language
English
Published in
Vietnam Journal of Mathematics
Citation
- Kow, P.-Z., Salo, M., & Shahgholian, H. (2023). On Positivity Sets for Helmholtz Solutions. Vietnam Journal of Mathematics, 51(4), 985-994. https://doi.org/10.1007/s10013-023-00646-y
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Funder(s)
European Commission
Research Council of Finland
Funding program(s)
ERC Consolidator Grant
Centre of Excellence, AoF
ERC Consolidator Grant
Huippuyksikkörahoitus, SA
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
This project was finalized while the authors stayed at Institute Mittag Leffler (Sweden), during the program Geometric aspects of nonlinear PDE. Kow and Salo were partly supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, 312121) and by the European Research Council under Horizon 2020 (ERC CoG 770924). Shahgholian was supported by Swedish Research Council.
Copyright© 2023 the Authors