Geodesic
Calderón’s inverse conductivity problem in the plane
Kari Astala1 ; Lassi Päivärinta1
1Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
Annals of mathematics, Tome 163 (2006) no. 1, pp. 265-299
Cet article a éte moissonné depuis la source Annals of Mathematics website

Voir la notice de l'article

We show that the Dirichlet to Neumann map for the equation $ \nabla\cdot\sigma\nabla u = 0$ in a two-dimensional domain uniquely determines the bounded measurable conductivity $ \sigma$. This gives a positive answer to a question of A. P. Calderón from 1980. Earlier the result has been shown only for conductivities that are sufficiently smooth. In higher dimensions the problem remains open.

DOI : 10.4007/annals.2006.163.265

Kari Astala  1   ; Lassi Päivärinta  1

1 Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland 
@article{10_4007_annals_2006_163_265,
     author = {Kari Astala and Lassi P\"aiv\"arinta},
     title = {Calder\'on{\textquoteright}s inverse conductivity problem in the plane},
     journal = {Annals of mathematics},
     pages = {265--299},
     year = {2006},
     volume = {163},
     number = {1},
     doi = {10.4007/annals.2006.163.265},
     mrnumber = {2195135},
     zbl = {1111.35004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.265/}
}
TY  - JOUR
AU  - Kari Astala
AU  - Lassi Päivärinta
TI  - Calderón’s inverse conductivity problem in the plane
JO  - Annals of mathematics
PY  - 2006
SP  - 265
EP  - 299
VL  - 163
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.265/
DO  - 10.4007/annals.2006.163.265
LA  - en
ID  - 10_4007_annals_2006_163_265
ER  - 
%0 Journal Article
%A Kari Astala
%A Lassi Päivärinta
%T Calderón’s inverse conductivity problem in the plane
%J Annals of mathematics
%D 2006
%P 265-299
%V 163
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.265/
%R 10.4007/annals.2006.163.265
%G en
%F 10_4007_annals_2006_163_265
Kari Astala; Lassi Päivärinta. Calderón’s inverse conductivity problem in the plane. Annals of mathematics, Tome 163 (2006) no. 1, pp. 265-299. doi: 10.4007/annals.2006.163.265

Cité par Sources :