Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data
<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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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2019
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| In: |
Inverse problems and imaging
Year: 2019, Jahrgang: 13, Heft: 5, Pages: 1023-1044 |
| ISSN: | 1930-8345 |
| DOI: | 10.3934/ipi.2019046 |
| Online-Zugang: | 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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| Verfasserangaben: | Angkana Rüland, Eva Sincich |
MARC
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| 520 | |a <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> | ||
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