The Neumann-to-Dirichlet map in two dimensions

Autor:	Masahiro Yamamoto, O. Yu. Imanuvilov, Gunther Uhlmann
Rok vydání:	2015
Předmět:	symbols.namesake Current (mathematics) General Mathematics Bounded function Dirichlet boundary condition Mathematical analysis Neumann boundary condition symbols Open set Boundary (topology) Uniqueness Domain (mathematical analysis) Mathematics
Zdroj:	Advances in Mathematics. 281:578-593
ISSN:	0001-8708
DOI:	10.1016/j.aim.2015.03.026
Popis:	For the two-dimensional Schrodinger equation in a bounded domain, we prove uniqueness of the determination of potentials in W p 1 ( Ω ) , p > 2 in the case where we apply all possible Neumann data supported on an arbitrarily non-empty open set Γ ˜ of the boundary and observe the corresponding Dirichlet data on Γ ˜ . An immediate consequence is that one can uniquely determine a conductivity in W p 3 ( Ω ) with p > 2 by measuring the voltage on an open subset of the boundary corresponding to a current supported in the same set.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ae5ab2cbe3e0a8129229f7c510921916 https://doi.org/10.1016/j.aim.2015.03.026 Zobrazit plný text záznamu Full Text from ScienceDirect