John圆与双曲度量

利用双曲度量讨论了John圆的几何性质,借助于Gehring-Hayman不等式建立了John圆的一个充要条件.     

John圆的可分解性质和拟圆的一个充要条件

证明D-R2是John圆当且仅当D具有John可分解性质;D-R2是拟圆当且仅当对于任意的z1,z2∈D,存在常数c≥1,使得1cλD(z1,z2)≤λD*(z1,z2)≤cλD(z1,z2).     

The Apollonian inner metric and uniform domains

In this paper we characterize uniform domains in terms of the Apollonian inner metric and the j‐metric, thus providing solutions to two open problems given in [16]. We also discuss the relationships among uniform, A‐uniform, Apollonian quasiconvex and quasi‐isotropic domains (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integrability of superharmonic functions, uniform domains, and Hölder domains

Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.

     

John 圆,拟圆及反射

利用内距离λD及构造的关于区域D的边界(a)D的反射RD得到了John 圆与拟圆的必要条件.     

The Riemannian Structure of John and Uniform Domains in ℝ<Superscript>n</Superscript>

Using the theory of pre-ends, we study the boundary and metric properties of John and uniform domains in the Euclidean n-space. We obtain some results on the metric Riemannian structure of these classes of domains. We prove that the family of John domains is closed under the class of homeomorphisms quasi-isometric in the intrinsic Riemannian metric and the family of uniform domains is closed under the class of bi-Lipschitz mappings.Original Russian Text Copyright © 2005 Karmazin A. P.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 786–804, July–August, 2005.     

Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups

This article completes the authors’s series on stability in the Liouville theorem on the Heisenberg group. We show that every mapping with bounded distortion on a John domain of the Heisenberg group is approximated by a conformal mapping with order of closeness √K ? 1 in the uniform norm and with order of closeness K ? 1 in the Sobolev L _p ¹ -norm for all p < C/K?1. We construct two examples, demonstrating the asymptotic sharpness of our results.     

Boundary value problems for the Laplacian in convex and semiconvex domains

We study the fully inhomogeneous Dirichlet problem for the Laplacian in bounded convex domains in Rn, when the size/smoothness of both the data and the solution are measured on scales of Besov and Triebel-Lizorkin spaces. As a preamble, we deal with the Dirichlet and Regularity problems for harmonic functions in convex domains, with optimal nontangential maximal function estimates. As a corollary, sharp estimates for the Green potential are obtained in a variety of contexts, including local Hardy spaces. A substantial part of this analysis applies to bounded semiconvex domains (i.e., Lipschitz domains satisfying a uniform exterior ball condition).     

Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces

In the setting of metric measure spaces equipped with a doubling measure supporting a weak p-Poincaré inequality with 1?p<∞, we show that any uniform domain Ω is an extension domain for the Newtonian space N1,p(Ω) and that Ω, together with the metric and the measure inherited from X, supports a weak p-Poincaré inequality. For p>1, we obtain a near characterization of N1,p-extension domains with local estimates for the extension operator.     

Biorthogonal bases with local support and approximation properties

We construct locally supported basis functions which are biorthogonal to conforming nodal finite element basis functions of degree in one dimension. In contrast to earlier approaches, these basis functions have the same support as the nodal finite element basis functions and reproduce the conforming finite element space of degree . Working with Gauß-Lobatto nodes, we find an interesting connection between biorthogonality and quadrature formulas. One important application of these newly constructed biorthogonal basis functions are two-dimensional mortar finite elements. The weak continuity condition of the constrained mortar space is realized in terms of our new dual bases. As a result, local static condensation can be applied which is very attractive from the numerical point of view. Numerical results are presented for cubic mortar finite elements.

     

The Solution of a Singularly Perturbed Convection–Diffusion Problem by an Iterative Domain Decomposition Method

This paper deals with an iterative algorithm for domain decomposition applied to the solution of a singularly perturbed convection–diffusion problem. Convergence properties of the algorithm are established. Numerical results are presented.     

区域上Besov空间的分子分解及其在偏微分方程中的应用

该文先刻划了外正则区域ΩR^n(n≥1)上Besov空间B^{s,p}_p(s<0,0相似文献   

Some topological and geometrical properties of the sequence space e (u,p)

In this paper, we introduce the sequence space e^r(u,p) and investigate its some topological and geometrical properties such as basis, α-, β-, γ- duals and the uniform Opial property.     

Synchronous and asynchronous optimized Schwarz methods for one‐way subdivision of bounded domains

Convergence of both synchronous and asynchronous optimized Schwarz algorithms for the shifted Laplacian operator on a bounded rectangular domain, in a one‐way subdivision of the computational domain, with overlap, is shown. Convergence results are obtained under very mild conditions on the size of the subdomains and on the amount of overlap. A couple of results are also given, relating the convergence rate of the asynchronous method to changes in the size of the domain. Numerical experiments illustrate the theoretical results.     

区域上Besov空间的原子分解和限制定理

本文在区域Ω（Ω 　 Ｒｎ，ｎ≥１）上定义了某类在边界上消失的Ｂｅｓｏｖ空 间Ｂ~（ｓ，ｑ）_（ｐ，ｏ）（Ω）（ｓ∈Ｒ，０＜ｐ，ｑ≤∞），并给出了它的原子分解，然后证明了当区域Ω∈ Ｄε（ｎ）（０＜ε≤１，ｐｓ＜ε）时，得到了限制定理Ｂ~（ｓ，ｑ）_（ｐ，ｏ）（Ω）＝Ｂ~（ｓ，ｑ）_（ｐ）（Ω）．     

Parabolicity and Hyperbolicity Conditions for Boundary Elements of Surfaces

Mathematical Notes -