On some partial data Calderón type problems with mixed boundary conditions
Abstract
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. The CGO solutions are constructed by duality to a new Carleman estimate.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Elsevier
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202110285432Use this for linking
Review status
Peer reviewed
ISSN
0022-0396
DOI
https://doi.org/10.1016/j.jde.2021.04.004
Language
English
Published in
Journal of Differential Equations
Citation
- Covi, G., & Rüland, A. (2021). On some partial data Calderón type problems with mixed boundary conditions. Journal of Differential Equations, 288, 141-203. https://doi.org/10.1016/j.jde.2021.04.004
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Funder(s)
European Commission
Funding program(s)
ERC Consolidator Grant
ERC Consolidator Grant
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 started during a visit of G. Covi to the MPI MIS. Both authors would like to thank the MPI MIS for the great working environment. Both authors would also like to thank Mikko Salo for pointing out the articles [28], [36] and some of the literature on the inverse Robin problem to them. G. Covi was partially supported by the European Research Council under Horizon 2020 (ERC CoG 770924). A. Rüland acknowledges that, after the submission of the article, she became a member of the Heidelberg STRUCTURES Excellence Cluster, which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC 2181/1 - 390900948.
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