相关论文: Global $C^\nf$ Irregularity of the $\bar\partial$-…

We establish sharp regularity and Fredholm theorems for the \bar{\partial}_b-Neumann problem on domains satisfying some non-generic geometric conditions. We use these domains to construct explicit examples of bad behaviour of the Kohn…

We give a potential theoretic characterization for compactness of the dbar-Neumann problem on smooth bounded pseudoconvex domains in C^n.

In the paper we give a lower estimate for the essential norm of the $\bar{\partial}$-Neumann operator on convex domains and worm domains of Diederich and Fornaess.

The $\bar{\partial}$-Neumann problem is the fundamental boundary value problem in several complex variables. It features an elliptic operator coupled with non-coercive boundary conditions. The problem is globally regular on many, but not…

For a domain $D$ of $\mathbb{C}^n$ which is weakly $q$-pseudoconvex or $q$-pseudoconcave we give a sufficient condition for subelliptic estimates for the $\bar{\partial}$-Neumann problem. The paper extends to domains which are not…

In this note, we find an equivalent boundary integral equation to the classical $\bar{\partial}$-Neumann problem. The new equation contains an equivalent regularity to the global regularity of the $\bar{\partial}$-Neumann problem. We also…

We construct higher-dimensional versions of the Diederich-Fornaess worm domains and show that the Bergman projection operators for these domains are not bounded on high-order $L^p$-Sobolev spaces for $1\leq p<\infty.$

We prove regularity of solutions of the $\bar\partial$-problem in the H\"older-Zygmund spaces of bounded, strongly $\mathbf C$-linearly convex domains of class $C^{1,1}$. The proofs rely on a new, analytic characterization of said domains…

We study the $\bar{\partial}_b$-Neumann problem for domains $\Omega$ contained in a strictly pseudoconvex manifold M^{2n+1} whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts…

A solution operator to the $\bar{\partial}$-equation is constructed on unbounded worm domains, $D_{\beta}$. Regularity estimates are proven showing the operator preserves regularity of the data. The operator may be viewed as a continuous…

This thesis deals with Partial Differential Equations in Several Complex Variables and especially focuses on a general estimate for the $\bar\partial$-Neumann problem on a domain which is $q$-pseudoconvex or $q$-pseudoconcave at a boundary…

The Diederich-Forn{\ae}ss worm domain, an important example of a smoothly bounded pseudoconvex domain without a Stein neighborhood basis, provides key counterexamples in the theory of Several Complex Variables. In this paper, we examine its…

We solve the $\partial \bar{\partial}$-problem for the differential forms of class $C^\infty$ with boundary value in currents sense defined on a contractible completely strictly pseudoconvex domain of a complex manifold.

Let $M$ be a strongly pseudoconvex complex $G$-manifold with compact quotient $M/G$. We provide a simple condition on forms $\alpha$ sufficient for the regular solvability of the equation $\square u=\alpha$ and other problems related to the…

We obtain weighted estimates for the $\bar{\partial}$-Neumann operator on intersections of two smooth strictly pseudoconvex domains in $\mathbb{C}^2$. The regularity estimates are described with the use of Sobolev norms with weights which…

In this paper we study the Neumann problem for a type of fully nonlinear second order elliptic partial differential equations on domains in $\mathbb{C}^{n}$ without any curvature assumptions on the domain.

This paper treats subelliptic estimates for the $\bar{\partial}$-Neumann problem on a class of domains known as regular coordinate domains. Our main result is that the largest subelliptic gain for a regular coordinate domain is bounded…

We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant…

We establish general sufficient conditions for exact (and global) regularity in the $\bar\partial$-Neumann problem on $(p,q)$-forms, $0 \leq p \leq n$ and $1\leq q \leq n$, on a pseudoconvex domain $\Omega$ with smooth boundary $b\Omega$ in…

In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain $\mathcal{W}_\mu$ and its truncated version $\mathcal{W}'_\mu$. We determine some orthogonal systems and show that they are not…