An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem
- 13 September 2001
- journal article
- correction
- Published by IOP Publishing in Inverse Problems
- Vol. 17 (5) , 1561-1563
- https://doi.org/10.1088/0266-5611/17/5/501
Abstract
In theorem 3.1 of this paper we presented an estimate for t (k) and μ(x, k) for k near zero. The statement of theorem 3.1 holds, but the proof contains two errors. We incorrectly stated that S0 = R1 for a general C2 domain Ω. This led to an erroneous formula (24). We prove below that the identity S0 = ½R1 holds when Ω is the unit disc. The proof of theorem 3.1 can then be corrected by reducing it to that case. We proved the (correct) estimate ||k||L(H1/2(∂Ω)) ≤ C | k | for small | k |. However, in the original proof k is an operator from H -1/2(∂Ω) to H1/2(∂Ω). We provide a new argument showing that the above estimate can be used. See full text for further details.Keywords
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