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

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Related projects

Ministry reporting: Yes

Reporting Year: 2021

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