The L^{2}\bar{\partial } -Cauchy problem on weakly q-pseudoconvex domains in Stein manifolds

Title:

The L^{2}\bar{\partial } -Cauchy problem on weakly q-pseudoconvex domains in Stein manifolds

Creator:

Saber, Sayed

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7ec34c9f-a5da-4ae5-9448-fb5b5678039d
uuid:7ec34c9f-a5da-4ae5-9448-fb5b5678039d
issn:0011-4642

Subject:

matematika, mathematics, \overline \partial operator, q-convex domain, Stein manifold, \overline \partial -Neumann operator, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let X be a Stein manifold of complex dimension n\geqslant 2 and \Omega \Subset X be a relatively compact domain with C^{2} smooth boundary in X. Assume that Ω is a weakly q-pseudoconvex domain in X. The purpose of this paper is to establish sufficient conditions for the closed range of \overline \partial on Ω. Moreover, we study the \overline \partial -problem on Ω. Specifically, we use the modified weight function method to study the weighted \overline \partial -problem with exact support in Ω. Our method relies on the L^{2} -estimates by Hörmander (1965) and by Kohn (1973)., Sayed Saber., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

739-745

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:3

Harvested from:

CDK

Metadata only:

false