no. 5-6
Partial Differential Equations
A remark on Lipschitz stability for inverse problems
[Une remarque sur la stabilité lipschitzienne pour les problèmes inverses]

Présenté par : the Editorial Board

Bourgeois, Laurent1
1 Laboratoire POEMS, ENSTA ParisTech, 828, boulevard des Maréchaux, 91762 Palaiseau cedex, France
Comptes Rendus. Mathématique, Tome 351 (2013) no. 5-6, pp. 187-190.

Une estimation abstraite de stabilité lipschitzienne est prouvée pour une certaine classe de problèmes inverses. Elle est ensuite appliquée à un problème inverse de reconstruction dʼindice de réfraction pour lʼéquation de Helmholtz.

An abstract Lipschitz stability estimate is proved for a class of inverse problems. It is then applied to the inverse medium problem for the Helmholtz equation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.04.004
Bourgeois, Laurent 1

1 Laboratoire POEMS, ENSTA ParisTech, 828, boulevard des Maréchaux, 91762 Palaiseau cedex, France 
@article{CRMATH_2013__351_5-6_187_0,
     author = {Bourgeois, Laurent},
     title = {A remark on {Lipschitz} stability for inverse problems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {187--190},
     publisher = {Elsevier},
     volume = {351},
     number = {5-6},
     year = {2013},
     doi = {10.1016/j.crma.2013.04.004},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.04.004/}
}
TY  - JOUR
AU  - Bourgeois, Laurent
TI  - A remark on Lipschitz stability for inverse problems
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 187
EP  - 190
VL  - 351
IS  - 5-6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.04.004/
DO  - 10.1016/j.crma.2013.04.004
LA  - en
ID  - CRMATH_2013__351_5-6_187_0
ER  - 
%0 Journal Article
%A Bourgeois, Laurent
%T A remark on Lipschitz stability for inverse problems
%J Comptes Rendus. Mathématique
%D 2013
%P 187-190
%V 351
%N 5-6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.04.004/
%R 10.1016/j.crma.2013.04.004
%G en
%F CRMATH_2013__351_5-6_187_0
Bourgeois, Laurent. A remark on Lipschitz stability for inverse problems. Comptes Rendus. Mathématique, Tome 351 (2013) no. 5-6, pp. 187-190. doi : 10.1016/j.crma.2013.04.004. http://www.numdam.org/articles/10.1016/j.crma.2013.04.004/

[1] Alessandrini, G. Stable determination of conductivity by boundary measurements, Appl. Anal., Volume 27 (1988) no. 1–3, pp. 153-172 (ISSN: 0003-6811) | DOI

[2] Alessandrini, G.; Vessella, S. Lipschitz stability for the inverse conductivity problem, Adv. Appl. Math., Volume 35 (2005) no. 2, pp. 207-241 http://www.sciencedirect.com/science/article/B6W9D-4G1GD1N-2/2/e81b5cf1da9ce12a6ef62ce492c16bc4 (ISSN: 0196-8858) | DOI

[3] Bourgeois, L. A remark on Lipschitz stability for inverse problems, 2012 (Tech. Rep. INRIA 8104)

[4] Colton, D.; Kress, R. Inverse Acoustic and Electromagnetic Scattering Theory, Appl. Math. Sci., vol. 93, Springer-Verlag, 1998

[5] Conca, C.; Cumsille, P.; Ortega, J.; Rosier, L. On the detection of a moving obstacle in an ideal fluid by a boundary measurement, Inverse Probl., Volume 24 (2008) no. 4, p. 045001 (ISSN: 0266-5611) | DOI

[6] Hähner, P. A periodic Faddeev-type solution operator, J. Differ. Equ., Volume 128 (1996) no. 1, pp. 300-308 (ISSN: 0022-0396) | DOI

[7] Hähner, P.; Hohage, T. New stability estimates for the inverse acoustic inhomogeneous medium problem and applications, SIAM J. Math. Anal., Volume 33 (2001) no. 3, pp. 670-685 (electronic) (ISSN: 0036-1410) | DOI

[8] Rondi, L. A remark on a paper by G. Alessandrini and S. Vessella: “Lipschitz stability for the inverse conductivity problem” [Adv. Appl. Math. 35 (2) (2005) 207–241, MR2152888], Adv. Appl. Math., Volume 36 (2006) no. 1, pp. 67-69 (ISSN: 0196-8858) | DOI

[9] Sincich, E. Lipschitz stability for the inverse Robin problem, Inverse Probl., Volume 23 (2007), pp. 1311-1326

[10] Stefanov, P. Stability of the inverse problem in potential scattering at fixed energy, Ann. Inst. Fourier (Grenoble), Volume 40 (1990) no. 4, pp. 867-884 (ISSN: 0373-0956)

[11] Uhlmann, G. Electrical impedance tomography and Calderonʼs problem, Inverse Probl., Volume 25 (2009) no. 12, p. 123011 http://stacks.iop.org/0266-5611/25/i=12/a=123011

Cité par Sources :