A note on the problem when FS-domains coincide with RB-domains

Strongly Semicontinuous Domains and Semi-FS Domains

We are mainly concerned with some special kinds of semicontinuous domains and relationships between them. New concepts of strongly semicontinuous domains, meet semicontinuous domains and semi-FS domains are introduced. It is shown that a dcpo L is strongly semicontinuous if and only if L is semicontinuous and meet semicontinuous. It is proved that semi-FS domains are strongly semicontinuous. So...

Fekete-Szegö Problem of Functions Associated with Hyperbolic Domains

In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

Metric spaces and FS-domains

In this article we give general conditions on ametric space to insure that the poset of closed formal balls is an FS-domain. © 2008 Elsevier B.V. All rights reserved.

Characterising FS domains by means of power domains

We present two characterisations of FS domains, using the upper and the lower power domain construction, respectively. These characterisations have a common structure and thus can be generalised from the two power constructions to arbitrary premonads. The resulting classes of domains are considered in general, and some special instances are studied in greater detail. They form classes of domain...

Note on Colon-Multiplication Domains

Regularity Problem on Lipschitz Domains

This paper contains two results on the Lp regularity problem on Lipschitz domains. For second order elliptic systems and 1 < p < ∞, we prove that the solvability of the Lp regularity problem is equivalent to that of the Lp ′ Dirichlet problem. For higher order elliptic equations and systems, we show that if p > 2, the solvability of the Lp regularity problem is equivalent to a weak reverse Höld...