Reconstruction of the Derivative of the Conductivity at the Boundary
| Autor: | Felipe Ponce-Vanegas |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Control and Optimization Current (mathematics) 010102 general mathematics Isotropy Boundary (topology) Directional derivative Conductivity 01 natural sciences Omega 010101 applied mathematics Combinatorics Modeling and Simulation Domain (ring theory) Calderón's Problem Boundary Determination Boundary Lebesgue Points Discrete Mathematics and Combinatorics Pharmacology (medical) Uniqueness 0101 mathematics Analysis |
| Zdroj: | BIRD: BCAM's Institutional Repository Data instname Inverse Problems and Imaging |
| Popis: | We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. The method of reconstruction works for isotropic conductivities with low regularity. This boundary determination for rough conductivities implies the uniqueness of the conductivity in the whole domain \begin{document}$ \Omega $\end{document} when it lies in \begin{document}$ W^{1+\frac{n-5}{2p}+, p}(\Omega) $\end{document} , for dimensions \begin{document}$ n\ge 5 $\end{document} and for \begin{document}$ n\le p . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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