no. 17-18
Mathematical Analysis/Complex Analysis
Optimal logarithmic estimates in Hardy–Sobolev spaces Hk,∞

Presented by: Gilles Lebeau

Chaabane, Slim1; Feki, Imed1
1 Faculté des sciences de Sfax, BP 1171, 3018 Sfax, Tunisie
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1001-1006.

We prove sharp logarithmic estimates of optimal type in the Hardy–Sobolev spaces Hk,∞ (k∈N∗), thus extending earlier cases. These estimations are used in particular to establish logarithmic stability results for the Cauchy problem and the inverse problem of the identification of Robin's coefficient by boundary measurements.

On montre des résultats de stabilité logarithmique de type optimal dans les espaces de Hardy–Sobolev Hk,∞ (k∈N∗). Ces estimations s'avèrent comme une extension des résultats déjà établis, et seront utilisées en particulier pour établir des résultats de stabilité logarithmique du problème de Cauchy et du problème inverse d'identification du coefficient de Robin par des mesures de surface.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.07.018
Chaabane, Slim 1; Feki, Imed 1

1 Faculté des sciences de Sfax, BP 1171, 3018 Sfax, Tunisie 
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Chaabane, Slim; Feki, Imed. Optimal logarithmic estimates in Hardy–Sobolev spaces $ {H}^{k,\infty }$. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1001-1006. doi : 10.1016/j.crma.2009.07.018. http://www.numdam.org/articles/10.1016/j.crma.2009.07.018/

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