Duke Mathematical Journal

Calderón inverse problem with partial data on Riemann surfaces

Colin Guillarmou and Leo Tzou

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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

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

First available in Project Euclid: 3 May 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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