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- W4300103526 abstract "Let $(Omega^3,g)$ be a compact smooth Riemannian manifold with smooth boundary and suppose that $U$ is a an open set in $Omega$ such that $g|_U$ is the Euclidean metric. Let $Gamma= overline{U} cap partial Omega$ be connected and suppose that $U$ is the convex hull of $Gamma$. We will study the uniqueness of an unknown potential for the Schr{o}dinger operator $ -triangle_g + q $ from the associated Dirichlet to Neumann map, $Lambda_q$. We will prove that if the potential $q$ is a priori explicitly known in $U^c$, then one can uniquely reconstruct $q$ over the convex hull of $Gamma$ from $Lambda_q$. We will also outline a reconstruction algorithm. More generally we will discuss the cases where $Gamma$ is not connected or $g|_{U}$ is conformally transversally anisotropic and derive the analogous result." @default.
- W4300103526 created "2022-10-03" @default.
- W4300103526 creator A5043286389 @default.
- W4300103526 date "2018-02-07" @default.
- W4300103526 modified "2023-09-28" @default.
- W4300103526 title "Uniqueness of a Potential from Boundary Data in Locally Conformally Transversally Anisotropic Geometries" @default.
- W4300103526 doi "https://doi.org/10.48550/arxiv.1802.02645" @default.
- W4300103526 hasPublicationYear "2018" @default.
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