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 editorsCovi, Giovanni; Rüland, Angkana

Journal or seriesJournal of Differential Equations

ISSN0022-0396

eISSN1090-2732

Publication year2021

Volume288

Pages range141-203

PublisherElsevier

Publication countryNetherlands

Publication languageEnglish

DOIhttps://doi.org/10.1016/j.jde.2021.04.004

Publication open accessNot open

Publication channel open accessChannel 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.


Keywordsinverse problemspartial differential equationsapproximationestimating (statistical methods)

Free keywordsinverse problems; (fractional) Calderón problem; partial data; runge approximation; complex geometrical optics solutions; Carleman estimates


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Ministry reportingYes

Reporting Year2021

JUFO rating2


Last updated on 2024-25-03 at 11:23