Brown, R. M. Recovering the conductivity at the boundary from the Dirichlet to Neumann map: A pointwise result. (English) Zbl 0991.35104 J. Inverse Ill-Posed Probl. 9, No. 6, 567-574 (2001). 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. Cited in 31 Documents 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 Keywords:pointwise reconstruction; nonsmooth conductivity; impedance tomography; elliptic operator; Dirichlet to Neumann map PDFBibTeX XMLCite \textit{R. M. Brown}, J. Inverse Ill-Posed Probl. 9, No. 6, 567--574 (2001; Zbl 0991.35104) Full Text: DOI