Graded pseudo-valuation domains

Abstract

We introduce a graded version of pseudo-valuation rings for integral domains graded by a torsionless monoid, and we extend several results to the graded situation.     

Automorphism group of exceptional symmetric domains RV

The exceptional symmetric Siegel domain RV(16) in C16 is defined. The exceptional classical domain (R)v(16)=τ(RV(16)) is computed, where τ is the Bergman mapping of the Siegel domain RV(16). And holomorphical automorphism group Aut (RV(16)) of the exceptional symmetric Siegel domain RV(16) is presented.     

Automorphism group of exceptional symmetric domains RVI

Here we give the definition of the exceptional symmetric Siegel domain R_VI(27) in C²⁷, and compute the exceptional symmetric domain ℛ_VI(27) = τ(R_VI(27)), where t is the Bergman mapping of the Siegel domainR _VI (27). Moreover, we present the holomorphical automorphism group Aut (ℛ_VI(27)) of the exceptional symmetric domain (ℛ_VI(27)).     

拟凸域上沿某些方向的边界 Schwarz 引理*

本文直接利用全纯映照的性质研究边界Schwarz引理,建立了拟凸域上沿某些满足正定条件的方向的边界Schwarz引理. 文章推广了强拟凸域情形的主要结果,但是证明的方法是不一样的.     

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.     

Automorphism group of exceptional symmetric domainsRV

The exceptional symmetric Siegel domainR _v(16) in ℂ¹⁶ is defined. The exceptional classical domain ℛ_v(16) = t(R_v(16)) is computed, where t is the Bergman mapping of the Siegel domain R_v(16). And holomorphical automorphism group Aut (R_v(16)) of the exceptional symmetric Siegel domainR _v(16) is presented     

Lp estimates of solutions tomixed boundary value problems for the Stokes system in polyhedral domains

A mixed boundary value problem for the Stokes system in a polyhedral domain is considered. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescribed on the faces of the polyhedron. The authors prove the existence of solutions in (weighted and non‐weighted) L_p Sobolev spaces and obtain regularity assertions for weak solutions. The results are based on point estimates of Green's matrix. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Remarks on Korn Inequalities

A recent joint paper with Doina Cioranescu and Julia Orlik was concerned with the homogenization of a linearized elasticity problem with inclusions and cracks(see[Cioranescu, D., Damlamian, A. and Orlik, J., Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptotic Analysis, 82, 2013, 201–232]). It required uniform estimates with respect to the homogenization parameter. A Korn inequality was used which involves unilateral terms on the boundaries where a nopenetration condition is imposed. In this paper, the author presents a general method to obtain many diverse Korn inequalities including the unilateral inequalities used in [Cioranescu, D., Damlamian, A. and Orlik, J., Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptotic Analysis, 82, 2013, 201–232]. A preliminary version was presented in [Damlamian, A., Some unilateral Korn inequalities with application to a contact problem with inclusions, C. R. Acad. Sci. Paris, Ser. I,350, 2012, 861–865].     

Extension Operators

We study the property of a domain of possesing extension operators bounded in the L²–norm of the gradients. We present known results as well as generalizations and refinements. We show how these results can be applied to the homogenization of perforated domains.     

Regular domains in homogeneous groups

We study John, uniform and non-tangentially accessible domains in homogeneous groups of steps 2 and 3. We show that domains in groups of step 2 are non-tangentially accessible and we give an explicit condition which ensures the John property in groups of step 3.

     

On the Minimal Solutions of Variational Inequalities in Orlicz-Sobolev Spaces

In this paper, the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains. She gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded domains. In both cases,coercive and noncoercive operators are handled. The sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established.     

Vector subspaces of finite fields and star operations on pseudo-valuation domains

Given an extension of finite fields $F\subseteq L$, we study the number of the equivalence classes of F-vector subspaces of L modulo multiplication by elements of L, obtaining an exact formula and some bounds. We then apply the results obtained to the study of the set of F-star operations on L, which correspond to star operations on a pseudo-valuation domain R.     

等维Cartan-Hartogs域双全纯映射的特征

本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域Ω^Bm(μ)不是球,则它上面存在一函数X使得它在Ω^Bm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维Cartan-Hartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域Ω^Bm(μ)不是球,Ω^Bm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变.     

NON-ISOTROPIC JACOBI SPECTRAL METHODS FOR UNBOUNDED DOMAINS

Some specific non-isotropic Jacobi approximations in multiple-dimensions are investigated, which are used for numerical solutions of differential equations on various unbounded domains. The convergence of proposed schemes are proved. Some efficient algorithms are provided. Numerical results are presented to illustrate the efficiency of this new approach.     

On Local ☆-Completely Integrally Closed Domains

Let ☆ be a star operation on an integral domain R. The domain R is a ☆-CICD if (AA ^?1)^☆ = R for all nonzero (fractional) ideals A of R. In this article, we prove that, if the maximal ideal of a local ☆-CICD is a ☆-ideal, then R is ☆-principal ideal domain. We also establish that any ☆-CICD R is locally a PID when ☆ is induced by the localizations at prime ideals of R.     

超越整函数稳定域的某些性质

讨论了有限个超越整函数fi(i=1,2,…,m)迭代生成的函数g=fm°fm-1°…°f1(z)游荡域的性质,在某些条件下,对Brannan和Hayman提出的一个问题给出了肯定的回答.此外,给出了g(z)稳定域有界的一个条件.     

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.     

Positive solutions for a class of multiparameter ordinary elliptic systems

Using a fixed point theorem due to M.A. Krasnosel'skii, the upper-lower solutions method and fixed point index theory, we study existence, non-existence and multiplicity of positive solutions for a class of systems of second-order ordinary differential equations. We give a new notion of superlinearity for nonlinearities. Observe that the nonlinearities may even be, in some sense, singular. As an application, we show multiplicity results for a class of semilinear elliptic systems in both bounded annular domains and exterior domains. In addition, we apply our results to fourth-order boundary value problems.     

拟Z-连续domain和Z-交连续domain

对一般子集系统Z,引入了Rudin性质、拟Z-连续domain及Z-交连续 domain的概念,讨论了它们的基本性质.特别是Z-连续性、拟Z-连续性、 Z-交连 续性和Z-Lawson拓扑之T2性之间的相互关系. 证明了当子集系统Z满足一定条件 时,拟Z-连续domain P上的Z-way below关系Z具有插入性质, P上的Z-Lawson 拓扑λZ(P)是T2的,且P可用Z-Lawson同态嵌入到某方体之中.文中给出了一个 domain P,其上的Lawson拓扑λ(P)是T2的,但P不是拟连续性domain.     

Weighted Hardy inequalities

For bounded Lipschitz domains D in it is known that if 1<p<∞, then for all β[0,β₀), where β₀=p−1>0, there is a constant c<∞ with

for all . We show that if D is merely assumed to be a bounded domain in that satisfies a Whitney cube-counting condition with exponent λ and has plump complement, then the same inequality holds with β₀ now taken to be . Further, we extend the known results (see [H. Brezis, M. Marcus, Hardy's inequalities revisited, Dedicated to Ennio De Giorgi, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997–1998) 217–237; M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev, A geometrical version of Hardy's inequality, J. Funct. Anal. 189 (2002) 537–548; J. Tidblom, A geometrical version of Hardy's inequality for W^1,p(Ω), Proc. Amer. Math. Soc. 132 (2004) 2265–2271]) concerning the improved Hardy inequality

c=c(n,p), by showing that the class of domains for which the inequality holds is larger than that of all bounded convex domains.