与双调和方程相关的连续模和Heinz-Schwarz型不等式

对于给定的两个正整数n≥2和m≥1,假设函数f满足如下条件:(1)在B~n内满足非齐次双调和方程■;(2)在■上满足■,以及■,其中■表示内法线方向导数,■表示■中的单位球以及■表示■的边界.本文主要研究/的连续模和Heinz-Schwarz型不等式.     

双调和型抛物方程的Schauder估计

该文给出了双调和型抛物方程初值问题解的Schauder估计,并且在适当的空间中证明了解的存在性与惟一性．类似于二阶情形,首先通过Fourier变换得到一个形式解,然后再利用位势理论和逼近方法得到解的正则性、唯一性及存在性．该方法简单而易懂．     

G型方程与GRONWALL型不等式

在本世纪初,T.H.Gronwall[1]建立了基本不等式如下:a(t),u(t)为[0,T]上非负连续函数,k 为非负常数,则由u(t)≤k+(?)a(s)u(s)ds,t∈[0,T]可以推出不等式u(t)≤kexp((?)a(s)ds),t∈[0,T].1956年,I.Bihari[2]得到推广的结果如下:     

$p$-双调和算子的第一特征值的等周上界和 Reilly 型不等式

在本文中,我们给出了嵌入到欧氏空间中的$n$维闭超曲面上$p$-双调和算子的第一特征值的一些等周上界.我们也给出了浸入到高维流形如欧氏空间,球面和射影空间中的闭子流形上$p$-双调和算子的第一特征值的一些Reilly-型不等式.     

有界洞型区域内双调和方程边值问题的可解性

这篇文章利用不动点定理证明了有界洞型区域内双调和方程边值问题正解的存在性及唯一性.并对解的不存在情形进行了研究.     

一个双调和方程的Schwarz交替法

设Ω为IR~2平面上的有界区域,其边界(?)Ω适当光滑,考虑四阶调和方程: △~2表示双调和算子,f∈L~2(Ω).(1.1)式的物理模型为简支板的平衡方程,问题解的存在唯一性在[5]中已有证明.     

双调和方程边值问题正解的研究

本以不动点原理为主要工具,证明了一类双调和方程正解的存在性。     

一类双调和方程的多解性

本文研究了非线性项在无穷远处次线性增长的一类双调和方程解的存在性和多解性.应用抽象临界点定理,证明了此类双调和方程至少有三个弱解存在.     

双调和方程边值问题正解的研究

本文以不动点原理为主要工具 ,证明了一类双调和方程正解的存在性 .     

一类双调和方程的可解性

利用上下解方法、嵌入定理和Leray-schauder不动点定理证明了一类双调和方程弱解的存在性定理.做为定理的应用,给出了一个实例.     

The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral

We study the unique solvability of the Dirichlet problem for the biharmonic equation in the exterior of a compact set under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight |x|^a. Depending on the value of the parameter ^a,a we prove uniqueness theorems or present exact formulas for the dimension of the solution space of the Dirichlet problem.     

单侧障碍问题解梯度的Hlder连续性

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关于Wiener过程泛函连续模的精确收敛速度

设{W（t）,t≥0}是一标准Wiener过程,记S是Strassen重对数律的紧集类·本文中我们讨论了两个变量sup_0≤t≤1-h inf_f∈S sup_0≤x≤1 |(W(t+hx)-W(t))(2h log h^-1)^-1/2 - f(x)|及inf_0≤t≤1-h sup_0≤x≤1 |(W(t + hx) - W(t))(2hlogh^-1)^-1/2- f(x)|（对任何f∈S）趋于零的精确的收敛速度.作为一个推广,我们建立了Wiener过程的不可微模与泛函的连续模之间的一种关系.     

Modulus of Continuity of Piecewise Analytic Functions

We obtain conditions under which the modulus of continuity of a piecewise analytic function given on a closed interval of the real axis is an analytic function in a neighborhood of zero.     

Brownian Continuity Modulus Via Series Expansions

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关于Bernstein-Kantorovich算子的Steckin-Marchaud型不等式

§1. Introduction For the Bernstein PolynomialsBn(f,x)=∑nk=0nkxk(1-x)n-ffkn,(1.1)Ditzian［1］ proved a pointwise approximation:Bn(f,x)-f(x)≤Cω2φλf,φ1-λ(x)n, 0≤λ≤1, φ(x)=x(1-x),(1.2)which unified the classical estimate for λ=0 and the norm estimate for λ=1. As the inverse result, Erich Van Wickeren［2］ proved:ω2α(f,n-1/2)≤Mαn-1∑nk=1Bkf-fα.But, this is only a norm estimate (with ω2φ(f,t)), not inclusive of the classical estimate (with ω2(f,t)). For f∈C［0,1］, the …     

The Regularity for Solutions of Variational Inequalities

The regularity for solutions of elliptic equations is rather perfectly solved. But it does not so perfect for that of elliptic variational inequalities. In literature only different special situations are considered. Now the boundedness, C^{0,λ} continuity and C^{1,α} regularity are proved for solutions of one-sided obstacle problems under more general structural conditions, in which the growth orders of u are permitted to reach the critical exponents and the growth order ϒ of the gradient in D is permitted to be super critical as 1 < p < n.     

Heisenberg型群上一类精确Hardy型不等式和Hardy-Sobolev型不等式及应用(英文)

本文在Heisenberg型群上建立了一类精确的Hardy型不等式。采用的技巧是逼近及正则化的方法。进一步利用这个结果,本文建立了一类精确的Hardy-Sobolev型不等式。这两个结果包括了已有的相关结果。作为应用,讨论了一类具有Hardy位势的非线性算子的正定性与下无界性。     

Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Classes Close to L 1

We establish a number of results on the integrability of the entropy and the weak solutions of the Dirichlet problem for nonlinear elliptic equations of second order depending on the integrability properties of the right-hand sides of these equations.     

Functional Modulus of Continuity for Brownian Motion in Holder Norm

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