Duke Mathematical Journal

Calderón inverse problem with partial data on Riemann surfaces

Colin Guillarmou and Leo Tzou

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Abstract

On a fixed smooth compact Riemann surface with boundary (M0,g), we show that, for the Schrödinger operator Δg+V with potential VC1,α(M0) for some α>0, the Dirichlet-to-Neumann map N|Γ measured on an open set ΓM0 determines uniquely the potential V. We also discuss briefly the corresponding consequences for potential scattering at zero frequency on Riemann surfaces with either asymptotically Euclidean or asymptotically hyperbolic ends.

Article information

Source
Duke Math. J., Volume 158, Number 1 (2011), 83-120.

Dates
First available in Project Euclid: 3 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1304429494

Digital Object Identifier
doi:10.1215/00127094-1276310

Mathematical Reviews number (MathSciNet)
MR2794369

Zentralblatt MATH identifier
1222.35212

Subjects
Primary: 35R30: Inverse problems
Secondary: 58J32: Boundary value problems on manifolds

Citation

Guillarmou, Colin; Tzou, Leo. Calderón inverse problem with partial data on Riemann surfaces. Duke Math. J. 158 (2011), no. 1, 83--120. doi:10.1215/00127094-1276310. https://projecteuclid.org/euclid.dmj/1304429494


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