Geodesic
Solutions to $\overline{\partial}$-equations on strongly pseudo-convex domains with $L^p$-estimates
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We construct a solution to the $\bar{\partial}$-equation on a strongly pseudo-convex domain of a complex manifold. This is done for forms of type $(0,s), s\geq 1 $, with values in a holomorphic vector bundle which is Nakano positive and for complex valued forms of type $(r,s), 1\leq r\leq n$, when the complex manifold is a Stein manifold. Using Kerzman's techniques, we find the $L^p$-estimates, $1\leq p\leq \infty$, for the solution.
Classification : 32F27, 32C35, 35N15
Keywords: L^p-estimates, $\bar{\partial}$-equation, strongly pseudo-convex, smooth boundary, complex manifolds 
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     author = {Abdelkader, Osama and Khidr, Shaban},
     title = {Solutions to $\overline{\partial}$-equations on strongly pseudo-convex domains with $L^p$-estimates},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a117/}
}
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Abdelkader, Osama; Khidr, Shaban. Solutions to $\overline{\partial}$-equations on strongly pseudo-convex domains with $L^p$-estimates. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a117/