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Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data

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<p style='text-indent:20px;'>In this note we discuss the conditional stability issue for the finite dimensional Calderón problem for the fractional Schrödinger equation with a finite number of measurements. More precisely, we assume that the unknown potential <inline-formula>...

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Bibliographic Details
Main Authors: Rüland, Angkana (Author) , Sincich, Eva (Author)
Format: Article (Journal)
Language:English
Published: 2019
In: Inverse problems and imaging
Year: 2019, Volume: 13, Issue: 5, Pages: 1023-1044
ISSN:1930-8345
DOI:10.3934/ipi.2019046
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.3934/ipi.2019046
Verlag, lizenzpflichtig, Volltext: https://www.aimsciences.org/article/doi/10.3934/ipi.2019046
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Author Notes:Angkana Rüland, Eva Sincich
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Summary:<p style='text-indent:20px;'>In this note we discuss the conditional stability issue for the finite dimensional Calderón problem for the fractional Schrödinger equation with a finite number of measurements. More precisely, we assume that the unknown potential <inline-formula><tex-math id="M1">\begin{document}$ q \in L^{\infty}(\Omega) $\end{document}</tex-math></inline-formula> in the equation <inline-formula><tex-math id="M2">\begin{document}$ ((- \Delta)^s+ q)u = 0 \mbox{ in } \Omega\subset \mathbb{R}^n $\end{document}</tex-math></inline-formula> satisfies the a priori assumption that it is contained in a finite dimensional subspace of <inline-formula><tex-math id="M3">\begin{document}$ L^{\infty}(\Omega) $\end{document}</tex-math></inline-formula>. Under this condition we prove Lipschitz stability estimates for the fractional Calderón problem by means of finitely many Cauchy data depending on <inline-formula><tex-math id="M4">\begin{document}$ q $\end{document}</tex-math></inline-formula>. We allow for the possibility of zero being a Dirichlet eigenvalue of the associated fractional Schrödinger equation. Our result relies on the strong Runge approximation property of the fractional Schrödinger equation.</p>
Item Description:Gesehen am 12.05.2021
Physical Description:Online Resource
ISSN:1930-8345
DOI:10.3934/ipi.2019046

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