no. 23-24
Partial Differential Equations/Mathematical Problems in Mechanics
Hölder stability estimates for some inverse pointwise source problems
[Stabilité Hölderienne pour un problème inverse de sources ponctuelles]
Présenté par : Philippe G. Ciarlet
El Badia, Abdellatif1 ; El Hajj, Ahmad1
1 Université de Technologie de Compiègne, LMAC, 60205 Compiègne cedex, France
Comptes Rendus. Mathématique, Tome 350 (2012) no. 23-24, pp. 1031-1035

In this Note we establish a Hölder stability estimate for an inverse pointwise source elliptic problem.

Nous établissons dans cette Note un résultat de stabilité Hölderienne dans un problème inverse de sources ponctuelles.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.11.006

El Badia, Abdellatif 1 ; El Hajj, Ahmad 1

1 Université de Technologie de Compiègne, LMAC, 60205 Compiègne cedex, France 
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El Badia, Abdellatif; El Hajj, Ahmad. Hölder stability estimates for some inverse pointwise source problems. Comptes Rendus. Mathématique, Tome 350 (2012) no. 23-24, pp. 1031-1035. doi: 10.1016/j.crma.2012.11.006

[1] Cannon, J.R.; Ewing, R.E. The locations and strengths of point sources, Improperly Posed Boundary Values Problems, Res. Notes Math., vol. 1, Pitman, London, 1975, pp. 39-53

[2] El Badia, A.; Ha-Duong, T. An inverse source problem in potential analysis, Inverse Problems, Volume 16 (2000), pp. 651-663

[3] El Badia, A.; Ha-Duong, T. On an inverse source problem for the heat equation. Application to a pollution detection problem, J. Inverse Ill-Posed Probl. (2002), pp. 585-599

[4] El Badia, A. Inverse source problem in an anisotropic medium by boundary measurements, Inverse Problems, Volume 21 (2005), pp. 1487-1506

[5] El Badia, A.; Nara, T. An inverse source problem for Helmholtzʼs equation from the Cauchy data with a single wave number, Inverse Problems, Volume 27 (2011), p. 105001

[6] O. Faugeras, F. Clment, R. Deriche, R. Kerivien, T. Papadoupolo, J. Roberts, T. Viville, F. Devernay, J. Gomes, G. Hermosillo, P. Kornprobst, D. Lingrand, The inverse EEG and MEG problems: The adjoint space approach I: The continuous case, Tech. Rep. 3673, INRIA, May 1999.

[7] Hämäläinen, M.; Hari, R.; Ilmoniemi, R.J.; Knuutila, J.; Lounasmaa, O.V. Magnetoencephalography – theory, instrumentation, and applications to noninvasive studies of the working human brain, Rev. Modern Phys., Volume 65 (1993), pp. 413-497

[8] Isakov, V. Applied Mathematical Sciences, Springer-Verlag, New York, 1998

[9] Kang, H.; Lee, H. Identification of simple poles via boundary measurements and application of EIT, Inverse Problems, Volume 20 (2004), pp. 1853-1863

[10] Rado, R. Factorization of even graphs, Quart. J. Math. Oxford Ser., Volume 20 (1949), pp. 95-104

[11] Vessella, S. Locations and strengths of point sources: stability estimates, Inverse Problems, Volume 8 (1992), pp. 911-917

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