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

Creator:
Saber, Sayed
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, \overline \partial operator, q-convex domain, Stein manifold, \overline \partial -Neumann operator, 13, and 51
Language:
English
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
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public