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.
Accepté le :
Publié le :
Laurent Bourgeois 1
@article{CRMATH_2013__351_5-6_187_0, author = {Laurent Bourgeois}, 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}, }
Laurent Bourgeois. A remark on Lipschitz stability for inverse problems. Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 187-190. doi : 10.1016/j.crma.2013.04.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.04.004/
[1] Stable determination of conductivity by boundary measurements, Appl. Anal., Volume 27 (1988) no. 1–3, pp. 153-172 (ISSN: 0003-6811) | DOI
[2] 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] A remark on Lipschitz stability for inverse problems, 2012 (Tech. Rep. INRIA 8104)
[4] Inverse Acoustic and Electromagnetic Scattering Theory, Appl. Math. Sci., vol. 93, Springer-Verlag, 1998
[5] 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] A periodic Faddeev-type solution operator, J. Differ. Equ., Volume 128 (1996) no. 1, pp. 300-308 (ISSN: 0022-0396) | DOI
[7] 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] 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] Lipschitz stability for the inverse Robin problem, Inverse Probl., Volume 23 (2007), pp. 1311-1326
[10] 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] 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 :
Commentaires - Politique