Geodesic
The Calderón problem with partial data
Carlos E. Kenig1 ; Johannes Sjöstrand2 ; Gunther Uhlmann3
1Department of Mathematics, University of Chicago, Chicago, IL 60637, United States and School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
2Centre de Mathématiques, École Polytechnique, 91128 Palaiseau, France
3Department of Mathematics, University of Washington, Seattle, WA 98195, United States
Annals of mathematics, Tome 165 (2007) no. 2, pp. 567-591
Cet article a éte moissonné depuis la source Annals of Mathematics website

Voir la notice de l'article

In this paper we improve an earlier result by Bukhgeim and Uhlmann [1] showing that in dimension $n\ge 3$, the knowledge of the Cauchy data for the Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of [1] but use a richer set of solutions to the Dirichlet problem. This implies a similar result for the problem of Electrical Impedance Tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary.

DOI : 10.4007/annals.2007.165.567

Carlos E. Kenig  1   ; Johannes Sjöstrand  2   ; Gunther Uhlmann  3

1 Department of Mathematics, University of Chicago, Chicago, IL 60637, United States and School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
2 Centre de Mathématiques, École Polytechnique, 91128 Palaiseau, France
3 Department of Mathematics, University of Washington, Seattle, WA 98195, United States 
@article{10_4007_annals_2007_165_567,
     author = {Carlos E. Kenig and Johannes Sj\"ostrand and Gunther Uhlmann},
     title = {The {Calder\'on} problem with partial data},
     journal = {Annals of mathematics},
     pages = {567--591},
     year = {2007},
     volume = {165},
     number = {2},
     doi = {10.4007/annals.2007.165.567},
     mrnumber = {2299741},
     zbl = {1127.35079},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.567/}
}
TY  - JOUR
AU  - Carlos E. Kenig
AU  - Johannes Sjöstrand
AU  - Gunther Uhlmann
TI  - The Calderón problem with partial data
JO  - Annals of mathematics
PY  - 2007
SP  - 567
EP  - 591
VL  - 165
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.567/
DO  - 10.4007/annals.2007.165.567
LA  - en
ID  - 10_4007_annals_2007_165_567
ER  - 
%0 Journal Article
%A Carlos E. Kenig
%A Johannes Sjöstrand
%A Gunther Uhlmann
%T The Calderón problem with partial data
%J Annals of mathematics
%D 2007
%P 567-591
%V 165
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.567/
%R 10.4007/annals.2007.165.567
%G en
%F 10_4007_annals_2007_165_567
Carlos E. Kenig; Johannes Sjöstrand; Gunther Uhlmann. The Calderón problem with partial data. Annals of mathematics, Tome 165 (2007) no. 2, pp. 567-591. doi: 10.4007/annals.2007.165.567

Cité par Sources :