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__a117,
     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__a117/}
}
TY  - JOUR
AU  - Abdelkader,  Osama
AU  - Khidr,  Shaban
TI  - Solutions to \(\overline{\partial}\)-equations on strongly pseudo-convex domains with \(L^p\)-estimates
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a117/
LA  - en
ID  - EJDE_2004__2004__a117
ER  - 
%0 Journal Article
%A Abdelkader,  Osama
%A Khidr,  Shaban
%T Solutions to \(\overline{\partial}\)-equations on strongly pseudo-convex domains with \(L^p\)-estimates
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a117/
%G en
%F EJDE_2004__2004__a117
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/