Global regularity of the $$\overline \partial$$ -neumann problem on an annulus between two pseudoconvex manifolds which satisfy property (P)problem on an annulus between two pseudoconvex manifolds which satisfy property (P)

1996 ◽  
Vol 90 (1) ◽  
pp. 437-448 ◽  
Author(s):  
Hong Rae Cho
Keyword(s):  
Neumann Problem ◽  
Global Regularity ◽  
Satisfy Property

Global regularity of the $$\bar \partial $$ -Neumann problem on circular domains

1989 ◽  
Vol 285 (1) ◽  
pp. 1-12 ◽  
Author(s):  
So-Chin Chen
Keyword(s):  
Neumann Problem ◽  
Global Regularity ◽  
Circular Domains

Global solvability and regularity for ∂¯ on an annulus between two weakly convex domains which satisfy property (P)

2019 ◽  
Vol 12 (03) ◽  
pp. 1950041
Author(s):  
Sayed Saber
Keyword(s):  
Neumann Problem ◽  
Complex Manifold ◽  
Global Solvability ◽  
Closed Formula ◽  
Convex Domains ◽  
Weakly Convex ◽  
Canonical Solution ◽  
Dimension Formula ◽  
Satisfy Property

Let [Formula: see text] be a complex manifold of dimension [Formula: see text] and let [Formula: see text]. Let [Formula: see text] be a weakly [Formula: see text]-convex and [Formula: see text] be a weakly [Formula: see text]-convex in [Formula: see text] with smooth boundaries such that [Formula: see text]. Assume that [Formula: see text] and [Formula: see text] satisfy property [Formula: see text]. Then the compactness estimate for [Formula: see text]-forms [Formula: see text] holds for the [Formula: see text]-Neumann problem on the annulus domain [Formula: see text]. Furthermore, if [Formula: see text] is [Formula: see text]-closed [Formula: see text]-form, which is [Formula: see text] on [Formula: see text] and which is cohomologous to zero on [Formula: see text], the canonical solution [Formula: see text] of the equation [Formula: see text] is smooth on [Formula: see text].

The Diederich–Fornaess index and the global regularity of the $$\bar{\partial }$$ ∂ ¯ -Neumann problem

2013 ◽  
Vol 276 (1-2) ◽  
pp. 93-113 ◽  
Author(s):  
Stefano Pinton ◽  
Giuseppe Zampieri
Keyword(s):  
Neumann Problem ◽  
Global Regularity

SOBOLEV ESTIMATES OF SOLUTIONS OF THE $\bar{\partial}$-NEUMANN PROBLEM ON PARAMETERS

2002 ◽  
Vol 13 (10) ◽  
pp. 1027-1042 ◽  
Author(s):  
SANGHYUN CHO
Keyword(s):  
Neumann Problem ◽  
Complex Manifold ◽  
Sobolev Spaces ◽  
Smooth Function ◽  
Global Regularity ◽  
Complex Structures ◽  
Estimates Of Solutions ◽  
Almost Complex Structures ◽  
Sobolev Estimates ◽  
Almost Complex

Let [Formula: see text] be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures {ℒτ}τ ∈ I, 0 ∈ I. Assume that there is a smooth function λ which is strictly plurisubharmonic with respect to the structure ℒ0 in a neighborhood of bM. Then we prove the global regularity for [Formula: see text]-Neumann problem in Sobolev spaces both in space and parameter variables.

Sign in / Sign up

Export Citation Format

Share Document