Inverse Conductivity Problem on Riemann Surfaces |
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Authors: | Gennadi Henkin Vincent Michel |
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Institution: | (1) Université Pierre et Marie Curie, Mathématiques, case 247, 4 place Jussieu, 75252 Paris, France |
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Abstract: | An electrical potential U on a bordered Riemann surface X with conductivity function σ>0 satisfies equation d(σ
d
c
U)=0. The problem of effective reconstruction of σ from electrical currents measurements (Dirichlet-to-Neumann mapping) on the boundary: U|
bX
↦
σ
d
c
U|
bX
is studied. We extend to the case of Riemann surfaces the reconstruction scheme given, firstly, by R. Novikov (Funkc. Anal.
Ego Priloz. 22:11–22, 2008) for simply connected X. We apply for this new kernels for
on the affine algebraic Riemann surfaces constructed in Henkin (, 2008).
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Keywords: | Riemann surface Electrical current Inverse conductivity problem " target="_blank">gif" alt="$\bar{ \partial }$" align="middle" border="0"> -method Homotopy formulas |
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