In this paper we study the isotropic realizability of a given non smooth gradient field defined in , namely when one can reconstruct an isotropic conductivity such that is divergence free in . On the one hand, in the case where is non-vanishing, uniformly continuous in and is a bounded function in , we prove the isotropic realizability of 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 is piecewise regular, we prove roughly speaking that the isotropic realizability holds if and only if the normal derivatives of on each side of the gradient discontinuity interfaces have the same sign. Some examples of conductivity reconstruction are given.
Mots-clés : Isotropic conductivity, electric field, conductivity reconstruction, gradient flow, triangulation
@article{M2AN_2018__52_3_1173_0, author = {Briane, Marc}, title = {Reconstruction of isotropic conductivities from non smooth electric fields}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1173--1193}, publisher = {EDP-Sciences}, volume = {52}, number = {3}, year = {2018}, doi = {10.1051/m2an/2018013}, zbl = {1402.35311}, mrnumber = {3865562}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2018013/} }
TY - JOUR AU - Briane, Marc TI - Reconstruction of isotropic conductivities from non smooth electric fields JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1173 EP - 1193 VL - 52 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2018013/ DO - 10.1051/m2an/2018013 LA - en ID - M2AN_2018__52_3_1173_0 ER -
%0 Journal Article %A Briane, Marc %T Reconstruction of isotropic conductivities from non smooth electric fields %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1173-1193 %V 52 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2018013/ %R 10.1051/m2an/2018013 %G en %F M2AN_2018__52_3_1173_0
Briane, Marc. Reconstruction of isotropic conductivities from non smooth electric fields. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 1173-1193. doi : 10.1051/m2an/2018013. http://archive.numdam.org/articles/10.1051/m2an/2018013/
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