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Calderón’s inverse conductivity problem in the plane. (English) Zbl 1111.35004
Summary: We show that the Dirichlet to Neumann map for the equation ·σu=0 in a two-dimensional domain uniquely determines the bounded measurable conductivity σ. This gives a positive answer to a question of A. P. Calderón from 1980. Earlier the result has been shown only for conductivities that are sufficiently smooth. In higher dimensions the problem remains open.

MSC:
35B30Dependence of solutions of PDE on initial and boundary data, parameters
30C62Quasiconformal mappings in the plane
35R30Inverse problems for PDE
35J25Second order elliptic equations, boundary value problems
35R05PDEs with discontinuous coefficients or data