In this note, we prove an -existence theorem for the -Neumann operator and the regularity for the -equation on an annulus type domain , where and are strictly pseudoconvex domains with smooth boundaries in a Stein manifold X of complex dimension , such that . Moreover, we obtain Hölder and estimates for the -equation on strictly pseudoconcave domains with smooth -boundaries in X.
Dans cette Note, nous démontrons un théorème dʼexistence pour lʼopérateur de Neumann et la régularité globale au bord de lʼéquation sur de domaine de type couronne où et sont des domaines strictement pseudo-convexes dont les bords sont réguliés dans une variété de Stein X de dimension complexe , tels que . De plus, nous obtenons des estimations de Hölder et , , pour sur des domaines strictement pseudo-concaves de frontière dans X.
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Shaban Khidr 1; Osama Abdelkader 2
@article{CRMATH_2013__351_23-24_883_0, author = {Shaban Khidr and Osama Abdelkader}, title = {Global regularity and $ {L}^{p}$-estimates for $ \overline{\partial }$ on an annulus between two strictly pseudoconvex domains in a {Stein} manifold}, journal = {Comptes Rendus. Math\'ematique}, pages = {883--888}, publisher = {Elsevier}, volume = {351}, number = {23-24}, year = {2013}, doi = {10.1016/j.crma.2013.10.020}, language = {en}, }
TY - JOUR AU - Shaban Khidr AU - Osama Abdelkader TI - Global regularity and $ {L}^{p}$-estimates for $ \overline{\partial }$ on an annulus between two strictly pseudoconvex domains in a Stein manifold JO - Comptes Rendus. Mathématique PY - 2013 SP - 883 EP - 888 VL - 351 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2013.10.020 LA - en ID - CRMATH_2013__351_23-24_883_0 ER -
%0 Journal Article %A Shaban Khidr %A Osama Abdelkader %T Global regularity and $ {L}^{p}$-estimates for $ \overline{\partial }$ on an annulus between two strictly pseudoconvex domains in a Stein manifold %J Comptes Rendus. Mathématique %D 2013 %P 883-888 %V 351 %N 23-24 %I Elsevier %R 10.1016/j.crma.2013.10.020 %G en %F CRMATH_2013__351_23-24_883_0
Shaban Khidr; Osama Abdelkader. Global regularity and $ {L}^{p}$-estimates for $ \overline{\partial }$ on an annulus between two strictly pseudoconvex domains in a Stein manifold. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 883-888. doi : 10.1016/j.crma.2013.10.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.020/
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