On Single Measurement Stability for the Fractional Calderón Problem

2020/07/27 by Rüland, Angkana
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.13624

Abstract

In this short note we prove the logarithmic stability of the single measurement uniqueness result for the fractional Calderón problem which had been derived in \citeGRSU18. To this end, we use the quantitative uniqueness results established in \citeRS20a and complement these bounds with a boundary doubling estimate. The latter yields control of the order of vanishing of solutions to the fractional Schrödinger equation. Then, following a scheme introduced in \citeS10,ASV13 in the context of the determination of a surface impedance from far field measurements, this allows us to deduce logarithmic stability of the potential q.

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