Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 73, pp. 1-9.
Title: Solutions to $\bar{\partial}$-equations on strongly
pseudo-convex domains with $L^p$-estimates
Authors: Osama Abdelkader (Minia Univ., El-Minia, Egypt)
Shaban Khidr (Cairo Univ., Beni- Suef, Egypt)
Abstract:
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.
Submitted March 01, 2004. Published May 20, 2004.
Math Subject Classifications: 32F27, 32C35, 35N15.
Key Words: $L^p$-estimates; $\bar{\partial}$-equation; strongly pseudo-convex;
smooth boundary; complex manifolds.