Calderón’s inverse conductivity problem in the plane. (English) Zbl 1111.35004

Summary: We show that the Dirichlet to Neumann map for the equation \(\nabla\cdot \sigma\nabla u=0\) in a two-dimensional domain uniquely determines the bounded measurable conductivity \(\sigma\). 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.


35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
30C62 Quasiconformal mappings in the complex plane
35R30 Inverse problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
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