多元Sobolev关于Lqp（R^d）下的平均线性宽度

得到了两种多元Sobloev类于Lqp(R^d)下平均线笥宽度的弱渐估计。     

用样条逼近Sobolev函数类W_p~1(R)的逼近误差

作者研究了定义在全实轴上的Sobolev函数类W_p~1(R)的逼近问题.以一次样条函数作为逼近工具,给出了p=1和p=∞时的逼近误差.     

各向异性Sobolev及Besov类的平均单边宽度

给出了各向异性Sobolev类及各向异性Besov类的平均单边宽度,获得了相应的弱渐近估计.     

多元积分方程自适应解法的优化

考虑核属于各向异性的Sobolev类的积分方程自适应直接方法的优化,得到误差阶的精确估计及相应的最优方法.     

OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

This paper determines the exact error order on optimization of adaptive directmethods of approximate solution of the class of Fredholm integral equations of the secondkind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimalalgorithm.     

优化Sobolev体及其仿射性质

Sobolev不等式是联系分析和几何的基础不等式之一,而优化Sobolev体是优化Sobolev范数的临界几何核.首先,证明优化Sobolev体的一些仿射性质.然后,运用Barthe的优化迁移方法研究了凸体的特征函数和多胞形仿射函数的优化Sobolev体.     

广义周期Besov类在周期Sobolev空间中的宽度

本文给出了一种广义周期Besov类在周期Sobolev空间中的n-宽度的弱渐近估计。     

多元Fredholm积分方程自适应直接方法的优化

考虑了以各向异性光滑函数为核及自由项的多元Fredholm积分方程类的自适应直接方法的优化,得到误差阶的精确估计及相应的最优算法。     

单形积上的Sobolev类逼近问题的易处理性

我们在最大框架下研究定义于单纯形T~dR~d的m重积上的Sobolev类逼近问题的易处理性.对于信息类A~(all),得到了问题具有几种易处理性相匹配的充要条件,结果是依赖于问题参数的.本文是相应积分问题的继续研究.     

概率框架下一类算子方程逼近解的优化

引入概率框架下算子方程逼近解的优化问题, 证明了一个沟通算子方程在概率框架下的最优逼近解的阶与概率宽度渐近阶之间关系的一般性的结果, 并由此得到了以混合偏导数确定的多元Sobolev类中的函数为核的第二类Fredholm积分方程类在概率框架下最优逼近解的精确阶.     

Traces of Sobolev functions with one square integrable directional derivative

We consider the Sobolev spaces of square integrable functions v, from ?ⁿ or from one of its hyperquadrants Q, into a complex separable Hilbert space, with square integrable sum of derivatives ∑?_??v. In these spaces we define closed trace operators on the boundaries ?Q and on the hyperplanes {r_?? = z}, z ∈ ?\{0}, which turn out to be possibly unbounded with respect to the usual L²‐norm for the image. Therefore, we also introduce bigger trace spaces with weaker norms which allow to get bounded trace operators, and, even if these traces are not L², we prove an integration by parts formula on each hyperquadrant Q. Then we discuss surjectivity of our trace operators and we establish the relation between the regularity properties of a function on ?ⁿ and the regularity properties of its restrictions to the hyperquadrants Q. Copyright © 2005 John Wiley & Sons, Ltd.     

ON A MODIFIED SOBOLEV SPACE

In this note the author introduces a kind of Sobolev-type space called modified Sobolev space and deduce some fundamental properties of them.     

线性对流占优Sobolev方程的流线扩散有限元方法

Abastract. In this paper,a streamline-diffusion F. E. M. for linear Sobolev equations with con-vection-dominated term is given. According to the range of space-time F. E mesh parameter h,two choices for artifical diffusion parameter are presented,and for the corresponding computa-tion schemes the stability and error estimates in suitable norms are estabilished.     

高维广义积分子波变换及其性质

在Soblev空间上定义了一种新的广义积分子波变换,它包括了通常意义下的子波变换,付氏变换,R-变换,同时改进和延伸了朱在文献[1]中引入的广义积分子波变换等.并且对这种新的子波变换的基本性质进行了研究.     

The Initial Boundary Value Problem for the Flow of a Barotropic Viscous Fluid,Global in Time

AMS (MOS) Subject Classification 76N10, 35G30

The existence and uniqueness of solutions, in Sobolev spaces, of the initial boundary value problem, global in time for the set of equations describing the flow of a barotropic viscous gas is investigated. A proof is deduced only for the case of inflow into a bounded domain valid for small initial and boundary conditions.     

Sobolev方程的最小二乘Galerkin有限元法

本文对于Sobolev方程提出并分析了两种新型数值方法：最小二乘Galerkin有限元法．这种方法的优越性在于不需要验证LBB条件,可以更好的选择有限元空间．误差估计表明在L~2(Ω))~2×L~2(Ω)范数意义下,这两种方法均具有最优收敛阶,并且关于时间分别具有一阶精确度和二阶精确度．     

具临界Sobolev指数的半线性椭圆方程的多重正解

本文讨论了零边值半线性椭圆方程的多重正解，其中使用没有（ＰＳ）条件的山路引理及对最佳Ｓｏｂｏｌｅｖ嵌入常数的分析，证明了至少两个解的存在性．     

On the dynamics of a degenerate parabolic equation: global bifurcation of stationary states and convergence

We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary states, covering both the cases of a bounded and an unbounded domain. The global bifurcation of stationary states, implies-in conjuction with the definition of a gradient dynamical system in the natural phase space-that at least in the case of a bounded domain, any solution with nonnegative initial data tends to the trivial or the nonnegative equilibrium. Applications of the global bifurcation result to general degenerate semilinear as well as to quasilinear elliptic equations, are also discussed. Mathematics Subject Classification (1991) 35B40, 35B41, 35R05