Geodesic
Solutions to \(\overline{\partial}\)-equations on strongly pseudo-convex domains with \(L^p\)-estimates
Electronic journal of differential equations, Tome 2004 (2004)
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 
@article{EJDE_2004__2004__a17,
     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},
     year = {2004},
     volume = {2004},
     zbl = {1060.32022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a17/}
}
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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__a17/