π－正则半群的子直积

本文给出π－正则半群的子直积的构造，利用这一构造定理，研究π－正则半群的Ｅ－酉覆盖。     

基本的弱正则*-半群的结构

本文给出了基本的弱正则＊－半群的一个结构定理．作为这一结构定理的特 殊情形，基本的正则＊－半群的一个新的结构被给出．     

π—正则半群的子直积

本文给出了π－正则半群的子直积的构造，利用这一构造定理，研究了π－正则半群的Ｅ－酉覆盖。     

关于β-正则与一致β-正则诱导极限

本文举出反例说明文献［７］中关于一致β－正则的充要条件是错误的，并分别给出了诱导极限为β－正则与一致β－正则的正确的充要条件．     

奇异M—矩阵的图相容弱正则分裂

设Ａ是奇异Ｍ－矩阵，Ａ＝Ｍ－Ｎ是Ａ的图相容弱正则分裂。本文研究迭代矩阵Ｍ＾－１Ｎ的谱性质，得到与迭代矩阵的指数有关的一个定理：ｉｎｄ０（Ａ）＝ｉｎｄ１（Ｍ＾－１Ｎ）．它推广了Ｈ．Ｓｃｈｎｅｉｄｅｒ和作者的结果。     

奇异M─矩阵的图相容弱正则分裂

设Ａ是奇异Ｍ－矩阵，Ａ＝Ｍ－Ｎ是Ａ的图相容弱正则分裂．本文研究迭代矩阵Ｍ－１Ｎ的谱性质，得到与迭代矩阵的指数有关的一个定理：ｉｎｄ０（Ａ）＝ｉｎｄ１（Ｍ－１Ｎ）．它推广了Ｈ．Ｓｃｈｎｅｉｄｅｒ和作者的结果．     

关于RC-正则环（英文）

我们利用related单位正则无刻画了正则环的比较结构，进而把文[2]定理中的related单位元推广到了related单位正则无，并给出了RC－正则环的一个局部特征．     

关于弱－θ－加细空间的闭L原象

本文证明了，当定义域空间是正则空间时，弱－θ－加细性在闭Ｌ映射下是逆保持的，并给出例子说明，去掉定义域空间的正则性，上述结论不成立。     

关于弱－θ－加细空间的闭L原象

本文证明了，当定义域空间是正则空间时，弱θ＾－－加细性在闭Ｌ映射下是逆保持的，并给出例子说明，去掉定义域空正则性，上述结论不成立。     

关于NF-环的构造

研究了无限的ＮＦ－环及有限的ＮＦ－环，并且给出了有限ＮＦ－环的构造．     

Nontrivial solutions for Monge-Ampère type operators in convex domains

In this paper we prove existence and interior regularity of convex solutions of the Dirichlet problem for a class of Monge-Ampère type equations with right hand side vanishing on the boundary, by means of the fixed point index theory for Bakelman's weak solutions. The regularity in the interior follows from recent results of Caffarelli. Partially supported by M.U.R.S.T., Italy Partially supported by G.N.A.F.A. of C.N.R., Italy. This work was accomplished during a Humbold research stay at Karlsruhe and Heidelberg Universities.     

Quasi-Norm interpolation error estimates for the piecewise linear finite element approximation of p-Laplacian problems

Summary. In this work, new interpolation error estimates have been derived for some well-known interpolators in the quasi-norms. The estimates are found to be essential to obtain the optimal a priori error bounds under the weakened regularity conditions for the piecewise linear finite element approximation of a class of degenerate equations. In particular, by using these estimates, we can close the existing gap between the regularity required for deriving the optimal error bounds and the regularity achievable for the smooth data for the 2-d and 3-d p-Laplacian.Mathematics Subject Classification (1991): 65N30     

Quasiminimi di alcuni funzionali degeneri

Summary We prove regularity results for quasiminima of a class of degenerate functionals using weighted Sobolev estimates. For vector valued minima of some degenerate quadratic functionals a partial regularity result is also given.

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Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.     

算子值傅里叶乘子与向量值边值问题最大正则性

向量值L^p空间上的算子值傅里叶乘子由于L．Weis在2000年的重要工作而成为泛函分析的热点之一，其对R-有界性创造性的应用使这个领域的研究耳目一新，新的结果层出不穷．本文的目的是介绍算子值傅里叶乘子的这些最新进展，以及它们在向量值边值问题最大正则性方面的应用．包括N．J．Kalton和G．Lancien给出的关于L^p-最大正则性的反例．Besov空间和Triebel空间上的算子值傅里叶乘子以及在Besov空问和Triebel空间意义下的最大正则性也是我们要介绍的内容．     

On Metric Regularity and the Boundary of the Feasible Set in Linear Optimization

This paper deals with semi-infinite linear inequality systems in ? ⁿ and studies the stability of the boundary of their feasible sets. We analyze the equivalence between the metric regularity of the inverse of the boundary set mapping, $\mathcal{N}$ , and the stability of the feasible set mapping in the sense of the maintenance of the consistency. In doing this we provide operational formulae for distances from points to some useful sets. We also include relationships between the regularity moduli corresponding to the mappings $\mathcal{N}$ and the inverse, $\mathcal{M}$ , of the feasible set mapping, and prove their equality for finite systems and some special cases in the semi-infinite framework. Moreover, we provide conditions to assure that the metric regularity of $\mathcal{N}$ is equivalent to the lower semi-continuity of the boundary set mapping, which is important because the latter property has many characterizations. Since the boundary of a feasible set may not be convex, we cannot make use of the general theory for mappings with convex graph, as for example, the Robinson–Ursescu theorem.     

CONVERGENCE OF A MIXED FINITE ELEMENT FOR THE STOKES PROBLEM ON ANISOTROPIC MESHES

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works .     

Sulla regolarità della soluzione di un problema variazionale

Summary In this paper we study some regularity properties of a solution of a variational problem connected with a free boundary problem.

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Lavoro eseguito nell'ambito dell'Istituto per la Matematica Applicata del C.N.R. presso l'Università di Genova.     

On the regularity of discrete linear systems

In this paper we have introduced a new regularity coefficient of time varying discrete linear system. On the base of this coefficient we have characterized the regularity of homogeneous discrete time varying linear systems by nonhomogeneous ones. Moreover we provided bounds for the regularity coefficient in terms of the existing in the literature regularity coefficients.     

Stochastic Games for N Players

The objective of this paper is to present a useful application of the theory of regularity of systems of nonlinear partial differential equations to the solution of stochastic differential games with N players. It is particularly interesting to notice that the structure of games fits perfectly with what is requested to prove the regularity property which is needed.