The inverse conductivity problem with one measurement: uniqueness for convex polyhedra
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- by Bartolomé Barceló, Eugene Fabes and Jin Keun Seo
- Proc. Amer. Math. Soc. 122 (1994), 183-189
- DOI: https://doi.org/10.1090/S0002-9939-1994-1195476-6
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Abstract:
Let $\Omega$ denote a smooth domain in ${R^n}$ containing the closure of a convex polyhedron D. Set ${\chi _D}$ equal to the characteristic function of D. We find a flux g so that if u is the nonconstant solution of $\operatorname {div}\;((1 + {\chi _D})\nabla u) = 0$ in $\Omega$ with $\frac {{\partial u}}{{\partial n}} = g$ on $\partial \Omega$, then D is uniquely determined by the Cauchy data g and $f \equiv u/\partial \Omega$.References
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- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190, DOI 10.1007/978-3-642-61798-0 O. A. Ladyzenskaja and N. N. Ural’zeva, Linear and quasi-linear elliptic equations, Academic Press, London, 1968.
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 183-189
- MSC: Primary 35R30
- DOI: https://doi.org/10.1090/S0002-9939-1994-1195476-6
- MathSciNet review: 1195476