Towards a constructive method to determine an L∞-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a two dimensional body. We show that this equation depends directly on the measured data and has always a unique solution. This way the geometric optics solutions for the L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body.
@article{urn:eudml:doc:41788,
title = {A boundary integral equation for Calder\'on's inverse conductivity problem.},
journal = {Collectanea Mathematica},
volume = {57},
year = {2006},
pages = {127-139},
zbl = {1104.35068},
mrnumber = {MR2264207},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41788}
}
Astala, Kari; Päivärinta, Lassi. A boundary integral equation for Calderón's inverse conductivity problem.. Collectanea Mathematica, Tome 57 (2006) pp. 127-139. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41788/