## Duke Mathematical Journal

### Calderón inverse problem with partial data on Riemann surfaces

#### Abstract

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that, for the Schrödinger operator $\Delta_g+V$ with potential $V\in C^{1,\alpha}(M_0)$ for some $\alpha>0$, the Dirichlet-to-Neumann map $\mathcal{N}|_{\Gamma}$ measured on an open set $\Gamma\subset \partial M_0$ 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

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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