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arXiv · 1809.09272

Nachman's reconstruction for the Calderon problem with discontinuous conductivities

George Lytle·Peter Perry·Samuli Siltanen
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Abstract

We show that Nachman's integral equations for the Calder\'on problem, derived for conductivities in $W^{2,p}(\Omega)$, still hold for $L^\infty$ conductivities which are $1$ in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of $L^\infty$ conductivities. We rely on Astala-P\"aiv\"arinta's formulation of the Calder\'on problem for a framework in which these convergence results make sense.

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George Lytle, Peter Perry, Samuli Siltanen. 2018-09-25. Nachman's reconstruction for the Calderon problem with discontinuous conductivities. https://arxiv.org/abs/1809.09272

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