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On some partial data Calderón type problems with mixed boundary conditions

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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...

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Main Authors: Covi, Giovanni (Author) , Rüland, Angkana (Author)
Format: Article (Journal)
Language:English
Published: 15 April 2021
In: Journal of differential equations
Year: 2021, Volume: 288, Pages: 141-203
ISSN:1090-2732
DOI:10.1016/j.jde.2021.04.004
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jde.2021.04.004
Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0022039621002278
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Author Notes:Giovanni Covi, Angkana Rüland

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520 |a 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. 
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