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arXiv · 1805.00866

Lipschitz stability for the Finite Dimensional Fractional Calderón Problem with Finite Cauchy Data

Angkana Rüland·Eva Sincich
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Abstract

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 $q \in L^{\infty}(Ω) $ in the equation $((-Δ)^s+ q)u = 0 \mbox{ in } Ω\subset \mathbb{R}^n$ satisfies the a priori assumption that it is contained in a finite dimensional subspace of $L^{\infty}(Ω)$. Under this condition we prove Lipschitz stability estimates for the fractional Calderón problem by means of finitely many Cauchy data depending on $q$. 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.

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Angkana Rüland, Eva Sincich. 2018-05-02. Lipschitz stability for the Finite Dimensional Fractional Calderón Problem with Finite Cauchy Data. https://arxiv.org/abs/1805.00866

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