On the modulus of continuity of harmonic quasiregular mappings on the unit ball in Rn

Abstract

We show that, for a class of moduli functions ω(δ), 0 ≤ δ ≤ 2, the property, provided u is a quasiregular mapping. Our class of moduli functions includes ω(δ) = δ α (0 < α ≤ 1), so our result generalizes earlier results on Hölder continuity (see [1]) and Lipschitz continuity (see [2]).

On the quasiconformal self-mappings of the unit ball satisfying the Poisson differential equation

“…In this paper we continue to study the same problem in the space R n which was started in the paper [16]. See also [3], [4] and [5] for the related problem. The problem in the space is much more complicated because of the lack of the techniques of complex analysis.…”

Representation formula and bi-Lipschitz continuity of solutions to inhomogeneous biharmonic Dirichlet problems in the unit disk

“…The present article is motivated from the related studies in [7,18,23,26,28]. In [26], Olofsson considered the representation formula of the solutions to the following homogeneous biharmonic Dirichlet problem (briefly, HBDP in the following):…”

“…the boundary of B n ) in R n and P stands for the usual Poisson kernel with respect to ∆. The assumption "P [φ] being K-quasiregular" in [ [5,7,11,12,17,18,19,20,21,22,24,25,28,29] and the references therein for detailed discussions on this topic.…”

Moduli of continuity of harmonic quasiregular mappings on bounded domains

“…Harmonic quasiregular (briefly, hqr) mappings in the plane were studied first by Martio in [20], for a review of this subject and further results see [22] and references cited there. Moduli of continuity of harmonic quasiregular mappings in B n were studied by several authors, see [15,11,2]. In this paper, our main goal is to extended one of the main results from [1] to more general domains in R n .…”