On some partial data Calderón type problems with mixed boundary conditions
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
Published inJournal of Differential Equations
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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: 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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Related funder(s)European Commission
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Additional information about fundingThis 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 ,  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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