A1 Journal article (refereed)
On some partial data Calderón type problems with mixed boundary conditions (2021)
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
JYU authors or editors
Publication details
All authors or editors: Covi, Giovanni; Rüland, Angkana
Journal or series: Journal of Differential Equations
ISSN: 0022-0396
eISSN: 1090-2732
Publication year: 2021
Volume: 288
Pages range: 141-203
Publisher: Elsevier
Publication country: Netherlands
Publication language: English
DOI: https://doi.org/10.1016/j.jde.2021.04.004
Publication open access: Not open
Publication channel open access: Channel is not openly available
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/78403
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2006.03252
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.
Keywords: inverse problems; partial differential equations; approximation; estimating (statistical methods)
Free keywords: inverse problems; (fractional) Calderón problem; partial data; runge approximation; complex geometrical optics solutions; Carleman estimates
Contributing organizations
Related projects
- Inverse boundary problems - toward a unified theory
- Salo, Mikko
- European Commission
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 2