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.
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Abdellatif El Badia 1; Ahmad El Hajj 1
@article{CRMATH_2012__350_23-24_1031_0, author = {Abdellatif El Badia and Ahmad El Hajj}, title = {H\"older stability estimates for some inverse pointwise source problems}, journal = {Comptes Rendus. Math\'ematique}, pages = {1031--1035}, publisher = {Elsevier}, volume = {350}, number = {23-24}, year = {2012}, doi = {10.1016/j.crma.2012.11.006}, language = {en}, }
TY - JOUR AU - Abdellatif El Badia AU - Ahmad El Hajj TI - Hölder stability estimates for some inverse pointwise source problems JO - Comptes Rendus. Mathématique PY - 2012 SP - 1031 EP - 1035 VL - 350 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2012.11.006 LA - en ID - CRMATH_2012__350_23-24_1031_0 ER -
Abdellatif El Badia; Ahmad El Hajj. Hölder stability estimates for some inverse pointwise source problems. Comptes Rendus. Mathématique, Volume 350 (2012) no. 23-24, pp. 1031-1035. doi : 10.1016/j.crma.2012.11.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.11.006/
[1] The locations and strengths of point sources, Improperly Posed Boundary Values Problems, Res. Notes Math., vol. 1, Pitman, London, 1975, pp. 39-53
[2] An inverse source problem in potential analysis, Inverse Problems, Volume 16 (2000), pp. 651-663
[3] 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] Inverse source problem in an anisotropic medium by boundary measurements, Inverse Problems, Volume 21 (2005), pp. 1487-1506
[5] 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] Magnetoencephalography – theory, instrumentation, and applications to noninvasive studies of the working human brain, Rev. Modern Phys., Volume 65 (1993), pp. 413-497
[8] Applied Mathematical Sciences, Springer-Verlag, New York, 1998
[9] Identification of simple poles via boundary measurements and application of EIT, Inverse Problems, Volume 20 (2004), pp. 1853-1863
[10] Factorization of even graphs, Quart. J. Math. Oxford Ser., Volume 20 (1949), pp. 95-104
[11] Locations and strengths of point sources: stability estimates, Inverse Problems, Volume 8 (1992), pp. 911-917
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