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Date
2024-04Type
- Journal Article
ETH Bibliography
yes
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Abstract
We study the stability of an inverse problem for the fractional conductivity equationon bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problemunder suitable a priori bounds on the globally defined conductivities. The argument has three mainingredients: 1. the logarithmic stability of the related inverse problem for the fractional Schr\"odingerequation by R\"uland and Salo; 2. the Lipschitz stability of the exterior determination problem; 3.utilizing and identifying nonlocal analogies of Alessandrini's work on the stability of the classical Calder\'on problem. The main contribution of the article is the resolution of the technical difficulties related to the last mentioned step. Furthermore, we show the optimality of the logarithmic stabilityestimates, following the earlier works by Mandache on the instability of the inverse conductivity problem, and by R\"uland and Salo on the analogous problem for the fractional Schrodinger equation. Show more
Publication status
publishedExternal links
Journal / series
SIAM Journal on Mathematical AnalysisVolume
Pages / Article No.
Publisher
SIAMSubject
fractional Laplacian; fractional gradient; Calderón problem; conductivity equationMore
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ETH Bibliography
yes
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