Calderon inverse Problem with partial data on Riemann Surfaces

Colin Guillarmou (1) , Leo Tzou (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 Stanford University

On a fixed smooth compact Riemann surface with boundary $(M_0,g)$, we show that for the Schrödinger 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.

Domaines: Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]

Colin Guillarmou, Leo Tzou. Calderon inverse Problem with partial data on Riemann Surfaces. Duke Mathematical Journal, 2011, 158 (1), pp.83-120. ⟨hal-00409637v2⟩