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arXiv · 0908.1417

Calderon inverse Problem with partial data on Riemann Surfaces

Colin Guillarmou·Leo Tzou
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Abstract

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that for the Schrödinger operator $Δ+V$ with potential $V\in C^{1,α}(M_0)$ for some $α>0$, the Dirichlet-to-Neumann map $N|_Γ$ measured on an open set $Γ\subset \partial M_0$ 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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Colin Guillarmou, Leo Tzou. 2009-09-03. Calderon inverse Problem with partial data on Riemann Surfaces. https://doi.org/10.1215/00127094-1276310

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