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Proceedings of the American Mathematical Society

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The inverse conductivity problem with one measurement: uniqueness for convex polyhedra

Authors: Bartolomé Barceló, Eugene Fabes and Jin Keun Seo
Journal: Proc. Amer. Math. Soc. 122 (1994), 183-189
MSC: Primary 35R30
MathSciNet review: 1195476
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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 [Enhancements On Off] (What's this?)

  • [1] Avner Friedman and Victor Isakov, On the uniqueness in the inverse conductivity problem with one measurement, Indiana Univ. Math. J. 38 (1989), no. 3, 563–579. MR 1017325, 10.1512/iumj.1989.38.38027
  • [2] 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
  • [3] O. A. Ladyzenskaja and N. N. Ural'zeva, Linear and quasi-linear elliptic equations, Academic Press, London, 1968.

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Article copyright: © Copyright 1994 American Mathematical Society