Lipschitz stability for the finite dimensional fractional Calderón problem with finite cauchy data - Rüland, Angkana; Sincich, Eva (Arxiv, 2018)
In this note we discuss the conditional stability issue for the finite dimensional Calder\'on problem for the fractional Schrödinger equation with a finite number of measurements. More precisely, we assume that the unknown potential \in L^{∞}(Ω) $ in the equation $((-Δ)^s+ q)u = 0 in Ω\subset \mathbb{R}^n$ satisfies the a priori assumption that it is contained in a finite dimensional subspace of $L^{∞}(Ω)$. Under this condition we prove Lipschitz stability estimates for the fractional Calder\'on 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 Schr\"odinger equation. Our result relies on the strong Runge approximation property of the fractional Schr\"odinger equation.
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