Calderon inverse Problem with partial data on Riemann Surfaces

Details Calderon inverse Problem with partial data on Riemann Surfaces Calderon inverse Problem with partial data on Riemann Surfaces

2009-08-11

arxiv.org/abs/0908.1417v2

Mathematics

Analysis of PDEs

27 pages. Corrections and modifications in the Complex Geometric Optics solutions; regularity assumption strenghtened to $C^{1

Scientific paper

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that for the Schr\"odinger operator $\Delta +V$ with potential $V\in C^{1,\alpha}(M_0)$ for some $\alpha>0$, the Dirichlet-to-Neumann map $N|_{\Gamma}$ 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 0 frequency on Riemann surfaces with asymptotically Euclidean or asymptotically hyperbolic ends.

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