TY - JOUR
T1 - Lipschitz stability for the electrical impedance tomography problem
T2 - The complex case
AU - Beretta, Elena
AU - Francini, Elisa
PY - 2011/10
Y1 - 2011/10
N2 - where γ is a complex valued L∞ coefficient, satisfying a strong ellipticity condition. In electrical impedance tomography, γ represents the admittance of a conducting body. An interesting issue is the one of determining γ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map {n-ary logical and}γ. Under the above general assumptions this problem is an open issue. In this article we prove that, if we assume a priori that γ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of γ from {n-ary logical and}γ holds.
AB - where γ is a complex valued L∞ coefficient, satisfying a strong ellipticity condition. In electrical impedance tomography, γ represents the admittance of a conducting body. An interesting issue is the one of determining γ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map {n-ary logical and}γ. Under the above general assumptions this problem is an open issue. In this article we prove that, if we assume a priori that γ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of γ from {n-ary logical and}γ holds.
KW - Inverse admittivity problem
KW - Lipschitz continuous dependence
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U2 - 10.1080/03605302.2011.552930
DO - 10.1080/03605302.2011.552930
M3 - Article
AN - SCOPUS:80052586085
SN - 0360-5302
VL - 36
SP - 1723
EP - 1749
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 10
ER -