Volume 52, Number 3, May–June 2018
|Page(s)||1173 - 1193|
|Published online||14 September 2018|
Reconstruction of isotropic conductivities from non smooth electric fields
University of Rennes, INSA Rennes, CNRS, IRMAR – UMR 6625,
* Corresponding author: email@example.com
Accepted: 9 February 2018
In this paper we study the isotropic realizability of a given non smooth gradient field ∇u defined in ℝd, namely when one can reconstruct an isotropic conductivity σ > 0 such that σ∇u is divergence free in ℝd. On the one hand, in the case where ∇u is non-vanishing, uniformly continuous in ℝd and Δu is a bounded function in ℝd, we prove the isotropic realizability of ∇u using the associated gradient flow combined with the DiPerna, Lions approach for solving ordinary differential equations in suitable Sobolev spaces. On the other hand, in the case where ∇u is piecewise regular, we prove roughly speaking that the isotropic realizability holds if and only if the normal derivatives of u on each side of the gradient discontinuity interfaces have the same sign. Some examples of conductivity reconstruction are given.
Mathematics Subject Classification: 35B27 / 78A30 / 37C10
Key words: Isotropic conductivity / electric field / conductivity reconstruction / gradient flow / triangulation
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.