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The enclosure method and its applications. (English) Zbl 0988.35168

Saitoh, Saburou (ed.) et al., Analytic extension formulas and their applications. Dordrecht: Kluwer Academic Publishers. Int. Soc. Anal. Appl. Comput. 9, 87-103 (2001).
This paper is devoted to the inverse conductivity problem for \(\nabla\cdot \gamma\nabla u=0\) in a bounded domain \(\Omega\) from the Cauchy data on \(\partial \Omega\) of infinitely or finitely many solutions to the equation. To this end the author presents a new method which is based on exponentially growing solutions. Its application to the Cauchy problem for an elliptic equation and the Dirichlet problems are also considered.
For the entire collection see [Zbl 0963.00016].

MSC:

35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
35C15 Integral representations of solutions to PDEs
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