Nous montrons dans cette Note une inégalité de stabilité pour les problèmes de Cauchy elliptiques mal posés dans un domaine comportant des coins. Ce résultat complète un résultat antérieur obtenu pour un domaine régulier.
We prove in this Note a stability estimate for ill-posed elliptic Cauchy problems in a domain with corners. This result completes an earlier result obtained for a smooth domain.
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@article{CRMATH_2007__345_7_385_0, author = {Bourgeois, Laurent}, title = {A stability estimate for ill-posed elliptic {Cauchy} problems in a domain with corners}, journal = {Comptes Rendus. Math\'ematique}, pages = {385--390}, publisher = {Elsevier}, volume = {345}, number = {7}, year = {2007}, doi = {10.1016/j.crma.2007.09.014}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.09.014/} }
TY - JOUR AU - Bourgeois, Laurent TI - A stability estimate for ill-posed elliptic Cauchy problems in a domain with corners JO - Comptes Rendus. Mathématique PY - 2007 SP - 385 EP - 390 VL - 345 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.09.014/ DO - 10.1016/j.crma.2007.09.014 LA - en ID - CRMATH_2007__345_7_385_0 ER -
%0 Journal Article %A Bourgeois, Laurent %T A stability estimate for ill-posed elliptic Cauchy problems in a domain with corners %J Comptes Rendus. Mathématique %D 2007 %P 385-390 %V 345 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.09.014/ %R 10.1016/j.crma.2007.09.014 %G en %F CRMATH_2007__345_7_385_0
Bourgeois, Laurent. A stability estimate for ill-posed elliptic Cauchy problems in a domain with corners. Comptes Rendus. Mathématique, Tome 345 (2007) no. 7, pp. 385-390. doi : 10.1016/j.crma.2007.09.014. http://archive.numdam.org/articles/10.1016/j.crma.2007.09.014/
[1] L. Bourgeois, Conditional stability for ill-posed elliptic Cauchy problems in non-smooth domains, in preparation
[2] Prolongement unique des solutions de l'équation de Stokes, Communication in Partial Differential Equations, Volume 21 (1996), pp. 573-596
[3] Controllability of Evolution Equations, Lecture Notes Series, vol. 34, Research Institute of Math., Seoul National University, 1996
[4] Elliptic Problems in Nonsmooth Domains, Pitman, 1985
[5] Linear Partial Differential Operators, fourth printing, Springer-Verlag, 1976
[6] Contrôle exact de l'équation de la chaleur, Communication in Partial Differential Equations, Volume 20 (1995), pp. 335-356
[7] Les Méthodes Directes en Théorie Des équations elliptiques, Masson, 1967
[8] Remarques sur l'observabilité pour l'équation de Laplace, ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 621-635
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