The Calder\'on problem for the Schr\"odinger equation in transversally
anisotropic geometries with partial data
The Calder\'on problem for the Schr\"odinger equation in transversally
anisotropic geometries with partial data
We study the partial data Calder\'on problem for the anisotropic Schr\"{o}dinger equation \begin{equation} \label{eq: a1} (-\Delta_{\widetilde{g}}+V)u=0\text{ in }\Omega\times (0,\infty), \end{equation} where $\Omega\subset\mathbb{R}^n$ is a bounded smooth domain, $\widetilde{g}=g_{ij}(x)dx^{i}\otimes dx^j+dy\otimes dy$ and $V$ is translationally invariant in the $y$ direction. Our goal is to recover both the metric $g$ and the …