On the inner radius of univalency by pre-Schwarzian derivative

In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the lower bounds of inner radiuses for angular domains and strongly starlike domains are obtained.     

Some Bonnesen-style inequalities for higher dimensions

We discuss the higher dimensional Bonnesen-style inequalities.Though there are many Bonnesen-style inequalities for domains in the Euclidean plane R2 few results for general domain in R n(n ≥ 3) are known.The results obtained in this paper are for general domains,convex or non-convex,in Rn.     

Legendre Rational Spectral Method for Nonlinear Klein-Gordon Equation

1 Introduction The usual spectral methods are only available for di?erential equations on bounded domains. But it is also important to consider spectral methods for unbounded domains. For this purpose, we may use Hermite and Laguerre approximations on inf…     

Computations of Bergman Kernels on Hua Domains

The Bergman kernel function plays an important role in several complex variables. Thereexists the Bergman kernel function on any bounded domain in Cn. But we can get the Bergmankernel functions in explicit formulas for a few types of domains only, for example: the boundedhomogeneous domains and the egg domain in some cases.Yin Weiping defined four types of Hua domains:where RI(m, n), RII(p), RIII(q) and RIV(n) denote respectively the Cartan domains of first,second, third and fourth typ…     

A PRECONDITIONER FOR COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT AND COMPOSITE GRID FINITE ELEMENT

1. IntroductionThe coupling of boundary elemellts and finite elements is of great imPortance for the nu-mercal treatment of boundary value problems posed on unbounded domains. It permits us tocombine the advanages of boundary elements for treating domains extended to infinity withthose of finite elemenis in treating the comP1icated bounded domains.The standard procedure of coupling the boundary elemeni and finite elemeni methods isdescribed as follows. First, the (unbounded) domain is divided…     

解析簇上Leray-Stokes型积分表示公式（英文）

The closure of the bounded domains D in Cnconsists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in C~n, firstly using different method and technique we derive the corresponding integral representation formulas of differentiable functions for complex n-m(0 ≤ m n) dimensional analytic varieties in the two types of the bounded domains. Secondly we obtain the unified integral representation formulas of differentiable functions for complex n-m(0 ≤ m n) dimensional analytic varieties in the general bounded domains. When functions are holomorphic, the integral formulas in this paper include formulas of Stout~([1]), Hatziafratis~([2]) and the author~([3]),and are the extension of all the integral representations for holomorphic functions in the existing papers to analytic varieties. In particular, when m = 0, firstly we gave the integral representation formulas of differentiable functions for the two types of bounded domains in C~n. Therefore they can make the concretion of Leray-Stokes formula. Secondly we obtain the unified integral representation formulas of differentiable functions for general bounded domains in C~n. So they can make the Leray-Stokes formula generalizations.     

Homogenization of Elliptic Problems with Neumann Boundary Conditions in Non-smooth Domains

We consider a family of second-order elliptic operators {L_ε} in divergence form with rapidly oscillating and periodic coefficients in Lipschitz and convex domains in R~n. We are able to show that the uniform W~(1,p) estimate of second order elliptic systems holds for 2n/(n+1)-δ p 2n/(n-1)+ δ where δ 0 is independent of ε and the ranges are sharp for n = 2, 3. And for elliptic equations in Lipschitz domains, the W~(1,p) estimate is true for 3/2-δ p 3 + δ if n ≥ 4, similar estimate was extended to convex domains for 1 p ∞.     

A Prop erty of Convex Mappings on the Classical Domains

In this paper, we give a property of normalized biholomorphic convex mappings on the first, second and third classical domains： for any Z0 belongs to the classical domains, f maps each neighbourhood with the center Z0, which is contained in the classical domains, to a convex domain.     

Computations of Bergman Kernels on Hua Domains

The Bergman kernel function plays an important ro1e in several complex variables.There exists the Bergman kernel function on any bounded domain in Cn. But we can get the Bergman kernel functions in explicit formulas for a few types of domains only,for example:the bounded homogeneous domains and the egg domain in some cases.     

Some progress in spectral methods

In this paper,we review some results on the spectral methods.We frst consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems,including degenerated and singular diferential equations.Then we present the generalized Jacobi quasi-orthogonal approximation and its applications to the spectral element methods for high order problems with mixed inhomogeneous boundary conditions.We also discuss the related spectral methods for non-rectangular domains and the irrational spectral methods for unbounded domains.Next,we consider the Hermite spectral method and the generalized Hermite spectral method with their applications.Finally,we consider the Laguerre spectral method and the generalized Laguerre spectral method for many problems defned on unbounded domains.We also present the generalized Laguerre quasi-orthogonal approximation and its applications to certain problems of non-standard type and exterior problems.     

t-Schreier Domains

We study, under the name t-Schreier, the class of those integral domains whose group of t-invertible t-ideals satisfies the Riesz interpolation property. The so-called Prüfer v-multiplication domains (PVMDs) and Prüfer domains are special cases of t-Schreier domains. We show that, while a number of results known for Prüfer domains and PVMDs hold for these domains, the t-Schreier domains have a remarkable capability of unifying various results in that the results proved for t-Schreier domains can also be translated to results on pre-Schreier domains and hence on GCD and Bezout domains.     

Lipschitz Domains,Domains with Corners,and the Hodge Laplacian

ABSTRACT

We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains and form domains. We obtain results valid for general Lipschitz domains, and stronger results for a special class of “almost convex” domains, which apply to domains with corners.     

Uniform,Sobolev extension and quasiconformal circle domains

This paper contributes to the theory of uniform domains and Sobolev extension domains. We present new features of these domains and exhibit numerous relations among them. We examine two types of Sobolev extension domains, demonstrate their equivalence for bounded domains and generalize known sufficient geometric conditions for them. We observe that in the plane essentially all of these domains possess the trait that there is a quasiconformal self-homeomorphism of the extended plane which maps a given domain conformally onto a circle domain. We establish a geometric condition enjoyed by these plane domains which characterizes them among all quasicircle domains having no large and no small boundary components.     

Quadrature Domains with Infinite Volume

We discuss quadrature domains for subharmonic functions and prove the existence of core quadrature domains for certain positive measures. The core quadrature domains are the smallest quadrature domains as measures and inherit good properties from quadrature domains with finite volume. We next discuss new balayage for the class of harmonic functions integrable in a neighborhood of ∞. We give several estimates of balayage measures. The new balayage is introduced to construct quadrature domains for harmonic functions. Submitted: June 26, 2008. Accepted: July 24, 2008.     

Integral domains having a unique Kronecker function ring

We study the class of integrally closed domains having a unique Kronecker function ring, or equivalently, domains in which the completion (or b-operation) is the only e.a.b star operation of finite type. Such domains are a generalization of Prüfer domains and have fairly simple sets of valuation overrings. We give characterizations by studying valuation overrings and integral closure of finitely generated ideals. We provide new examples of such domains and show that for several well-known classes of integral domains the property of having a unique Kronecker function ring makes them fall into the class of Prüfer domains.     

Stratified two-stage sampling in domains: Sample allocation between domains, strata, and sampling stages

In the paper, formulae for optimum sample allocation between domains, strata in the domains, and sampling stages are presented for stratified two-stage sampling in domains under fixed sample size of SSUs from PSUs.     

Fine regularity for elliptic and parabolic anisotropic Robin problems with variable exponents

We investigate a class of quasi-linear elliptic and parabolic anisotropic problems with variable exponents over a general class of bounded non-smooth domains, which may include non-Lipschitz domains, such as domains with fractal boundary and rough domains. We obtain solvability and global regularity results for both the elliptic and parabolic Robin problem. Some a priori estimates, as well as fine properties for the corresponding nonlinear semigroups, are established. As a consequence, we generalize the global regularity theory for the Robin problem over non-smooth domains by extending it for the first time to the variable exponent case, and furthermore, to the anisotropic variable exponent case.     

Self-improving properties of inequalities of Poincaré type on measure spaces and applications

We show that the self-improving nature of Poincaré estimates persists for domains in rather general measure spaces. We consider both weak type and strong type inequalities, extending techniques of B. Franchi, C. Pérez and R. Wheeden. As an application in spaces of homogeneous type, we derive global Poincaré estimates for a class of domains with rough boundaries that we call ?-John domains, and we show that such domains have the requisite properties. This class includes John (or Boman) domains as well as s-John domains. Further applications appear in a companion paper.