Some stability inequalities for hybrid inverse problems

Mourad Choulli

doi:10.5802/crmath.262

Équations aux dérivées partielles

Some stability inequalities for hybrid inverse problems

Mourad Choulli ¹

¹ Université de Lorraine, France

Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1251-1265.

Résumé

We study some hybrid inverse problems associated to BVP’s for Schrödinger and Helmholtz type equations. The inverse problems we consider consist in the determination of coefficients from the knowledge of internal energy densities. We establish local Lipschitz stability inequalities as well as Hölder stability inequalities.

Reçu le : 2021-05-06
Révisé le : 2021-06-16
Accepté le : 2021-08-19
Publié le : 2022-01-04

DOI : 10.5802/crmath.262

Classification : 35R30

Affiliations des auteurs :

Mourad Choulli ¹

¹ Université de Lorraine, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2021__359_10_1251_0,
     author = {Mourad Choulli},
     title = {Some stability inequalities for hybrid inverse problems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1251--1265},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {10},
     year = {2021},
     doi = {10.5802/crmath.262},
     language = {en},
}

TY  - JOUR
AU  - Mourad Choulli
TI  - Some stability inequalities for hybrid inverse problems
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 1251
EP  - 1265
VL  - 359
IS  - 10
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.262
LA  - en
ID  - CRMATH_2021__359_10_1251_0
ER  -

%0 Journal Article
%A Mourad Choulli
%T Some stability inequalities for hybrid inverse problems
%J Comptes Rendus. Mathématique
%D 2021
%P 1251-1265
%V 359
%N 10
%I Académie des sciences, Paris
%R 10.5802/crmath.262
%G en
%F CRMATH_2021__359_10_1251_0

Mourad Choulli. Some stability inequalities for hybrid inverse problems. Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1251-1265. doi : 10.5802/crmath.262. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.262/

Bibliographie
Cité par

[1] Giovanni S. Alberti; Yves Capdeboscq Lectures on elliptic methods for hybrid inverse problems, Cours Spécialisés (Paris), 25, Société Mathématique de France, 2018

[2] Giovanni Alessandrini Global stability for a coupled physics inverse problem, Inverse Probl., Volume 30 (2014) no. 7, 075008, 10 pages | MR | Zbl

[3] Giovanni Alessandrini; Michele Di Cristo; Elisa Francini; Sergio Vessella Stability for quantitative photoacoustic tomography with well chosen illuminations, Ann. Mat. Pura Appl., Volume 196 (2017) no. 2, pp. 395-406 | DOI | MR | Zbl

[4] Giovanni Alessandrini; Vincenzo Nesi Quantitative estimates on Jacobians for hybrid inverse problems, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program., Volume 8 (2015) no. 3, pp. 25-41 | Zbl

[5] Habib Ammari; Yves Capdeboscq; Frédéric de Gournay; Anna Rozanova-Pierrat; Faouzi Triki Microwave imaging by elastic deformation, SIAM J. Appl. Math., Volume 71 (2011) no. 6, pp. 2112-2130 | DOI | MR | Zbl

[6] Guillaume Bal; Kui Ren; Gunther Uhlmann; Ting Zhou Quantitative thermo-acoustics and related problems, Inverse Probl., Volume 27 (2011) no. 5, 055007, 15 pages | MR | Zbl

[7] Guillaume Bal; John C. Schotland Inverse scattering and acousto-optic imaging, Phys. Rev. Lett., Volume 104 (2010), 043902 | DOI

[8] Guillaume Bal; Gunther Uhlmann Inverse diffusion theory of photoacoustics, Inverse Probl., Volume 26 (2010) no. 8, 085010, 20 pages | MR | Zbl

[9] Andrea Bonito; Albert Cohen; Ronald DeVore; Guergana Petrova; Gerrit Welper Diffusion coefficients estimation for elliptic partial differential equations, SIAM J. Math. Anal., Volume 49 (2017) no. 2, pp. 1570-1592 | DOI | MR | Zbl

[10] Eric Bonnetier; Mourad Choulli; Faouzi Triki Stability for quantitative photoacoustic tomography revisited (1905) (https://arxiv.org/abs/1905.07914)

[11] Mourad Choulli; Guanghui Hu; Masahiro Yamamoto Stability inequality for a semilinear elliptic inverse problem, NoDEA, Nonlinear Differ. Equ. Appl., Volume 28 (2021), 37, 26 pages | DOI | Zbl

[12] Mourad Choulli; Faouzi Triki New stability estimates for the inverse medium problem with internal data, SIAM J. Math. Anal., Volume 47 (2015) no. 3, pp. 1778-1799 | DOI | MR | Zbl

[13] Mourad Choulli; Faouzi Triki Hölder stability for an inverse medium problem with internal data, Res. Math. Sci., Volume 6 (2019) no. 1, 9, 15 pages | Zbl

[14] Nicola Garofalo; Fang-Hua Lin Unique continuation for elliptic operators: a geometric-variational approach, Commun. Pure Appl. Math., Volume 40 (1987) no. 3, pp. 347-366 | DOI | MR | Zbl

[15] David Gilbarg; Neil S. Trudinger Elliptic partial differential equations of second order, Springer, 1998

[16] Jacques-Louis Lions; Enrico Magenes Non-homogeneous boundary value problems and applications, Vol. I, Grundlehren der Mathematischen Wissenschaften, 18, Springer, 1972, xvi+357 pages

[17] Adrian Nachman; Alexandru Tamasan; Alexandre Timonov Conductivity imaging with a single measurement of boundary and interior data, Inverse Probl., Volume 23 (2007) no. 6, pp. 2551-2563 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique