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Recovering the conductivity at the boundary from the Dirichlet to Neumann map: A pointwise result. (English) Zbl 0991.35104

Summary: A formula is given for recovering the boundary values of the coefficient \(\gamma\) of an elliptic operator, \(\text{div} \gamma \nabla\), from the Dirichlet to Neumann map. The main point is that one may recover \(\gamma\) without any a priori smoothness assumptions. The formula allows one to recover the value of \(\gamma\) pointwise.

MSC:

35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35R05 PDEs with low regular coefficients and/or low regular data
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