Global Regularity for the ∂–Neumann Operator and Bounded Plurisubharmonic Exhaustion Functions
نویسندگان
چکیده
For a smooth, bounded, pseudoconvex domain Ω ⊂ C n , we derive a new sufficient condition for global regularity of the ¯ ∂-Neumann operator that generalizes McNeal's Property (˜ P), the approximately holomorphic vector fields of Boas and Straube, and a condition involving bounded plurisub-harmonic exhaustion functions due to Kohn.
منابع مشابه
The ∂̄-neumann Operator on Lipschitz Pseudoconvex Domains with Plurisubharmonic Defining Functions
On a bounded pseudoconvex domain in C with a plurisubharmonic Lipschitz defining function, we prove that the ∂̄-Neumann operator is bounded on Sobolev (1/2)-spaces. 0. Introduction LetD be a bounded pseudoconvex domain in C with the standard Hermitian metric. The ∂̄-Neumann operator N for (p, q)-forms is the inverse of the complex Laplacian = ∂̄ ∂̄∗ + ∂̄∗∂̄ , where ∂̄ is the maximal extension of the C...
متن کاملStrong Topological Regularity and Weak Regularity of Banach Algebras
In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...
متن کاملPlurisubharmonic Exhaustion Functions and Almost Complex Stein Structures
We prove that a relatively compact pseudoconvex domain with smooth boundary in an almost complex manifold admits a bounded strictly plurisubharmonic exhaustion function. We use this result in order to study convexity and hyperbolicity properties of these domains and the contact geometry of their boundaries.
متن کاملStability of Bounded Solutions for Degenerate Complex Monge-Ampère Equations
We show a stability estimate for the degenerate complex Monge-Ampère operator that generalizes a result of Ko lodziej [11]. In particular, we obtain the optimal stability exponent and also treat the case when the right hand side is a general Borel measure satisfying certain regularity conditions. Moreover our result holds for functions plurisubharmonic with respect to a big form generalizing th...
متن کاملRegularity and Boundary Behavior of Solutions to Complex Monge–ampère Equations
1. Background 5 2. Plurisubharmonic functions 8 3. The complex Monge–Ampère operator 10 3.1. Bedford’s and Taylor’s definition of the complex Monge–Ampère operator 11 3.2. Cegrell’s definition of the complex Monge–Ampère operator 12 4. The Dirichlet problem for the complex Monge–Ampère operator 14 4.1. Boundary blow-up problems for the complex Monge–Ampère operator 17 4.2. Comparison principles...
متن کامل