共查询到20条相似文献,搜索用时 93 毫秒
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胡俊云 《数学年刊A辑(中文版)》1996,(5)
本文讨论奇异Hammerstein型积分方程u λAFu=h1其中称该方程是奇异的,是指算子F的定义域不一定包含算子A的值域.利用Orlicz空间的一个嵌入性质,给出了奇异Hammerstein积分方程解的一个存在条件. 相似文献
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Clifford分析中于特征流形上奇异积分方程的正则化 总被引:1,自引:1,他引:0
黄沙 《数学物理学报(A辑)》1998,18(3):257-263
借助于多元复分析的思想,此文利用Clifford分析中于特征流形上奇异积分的两种Poincare'-Bretrand置换公式,研究特征流形上奇异积分方程的Fredhlom理论,找到了它的正则化算子. 相似文献
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在局部边界积分方程方法中,当源节点位于分析域的整体边界上时,局部边界积分将出现奇异积分问题,这些奇异积分需要做特别的处理.为此,提出了对域内节点采用局部积分方程,而对边界节点直接采用移动最小二乘近似函数引入边界条件来解决奇异积分问题,这同时也解决了对积分边界进行插值引入近似误差的问题.作为应用和数值实验,对Laplace方程和Helmholtz方程问题进行了分析,取得了很好的数值结果.进而,在Helmholtz方程求解中,采用了含波解信息的修正基函数来代替单项式基函数进行近似.数值结果显示,这样处理是简单高效的,在高波数声传播问题的求解中非常具有前景. 相似文献
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利用复双球面上的立体角系数的方法和置换公式,讨论复双球垒域上变系数奇异积分方程的正则化问题,推广了复超球面上变系数奇异积分方程的结论. 相似文献
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复超球面上的奇异积分方程 总被引:8,自引:0,他引:8
<正> 一维的奇异积分方程的理论已经相当完整,并有着极为广泛和重要的应用(例如参阅(?)高维的奇异积分方程还未完整.(?)写了一本关于高维奇异积分与奇异积分方程的书,总结了近年来的发展及其影响,从中可以看出,高维奇异积分方程距离完整还有一定的距离. 相似文献
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该文所讨论的是在Hadamard主值意义下,高阶奇异积分(犛犳)(狋)=∫ 犳(狓)(狓-狋)狀+1d狓, 狀≥1的小波逼近及数值计算.特别是当小波函数未知时,借助于方程(3.1),对高阶奇异积分作数值计算,建立了收敛性定理. 相似文献
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赵新泉 《数学物理学报(A辑)》1998,18(1):63-69
该文在[1]的基础上,进一步探讨了区间[-1,1]上带Cauchy核奇异积分方程权函数的分解及其解的稳定性和在Chebyshev模下的稳定性条件.证明了扰动方程的可解性及原方程的解对于已知函数的连续依赖性. 相似文献
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Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable. 相似文献
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Huoxiong Wu 《逼近论及其应用》2009,(3):230-241
In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 〈 p 〈 ∞, the L^p-boundedness of such operators are obtained provided that their kernels belong to the spaces L^q(s^n-1) for some q 〉 1. 相似文献
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A. B. Rasulov 《Differential Equations》2010,46(2):277-283
For a second-order elliptic system with a singular point, we obtain integral representations and inversion formulas for the
case in which the singular point is an interior point of the domain. In the integral representations, we clearly extract the
singular part of the solutions, which permits one to study the asymptotics of the solutions as r → 0. In addition, we give a well-posed statement of a number of boundary value problems. 相似文献
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Harun Karsli 《逼近论及其应用》2010,(2):140-152
In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form:Tλ(f;x)=B∫AKλ(t,x,f(t))dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as (x,λ) → (x0, λ0) in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23] 相似文献
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The paper is devoted to study of singular integral operators with
fixed singularities at endpoints of contours on weighted Lebesgue spaces with
general Muckenhoupt weights. Compactness of certain integral operators with
fixed singularities is established. The membership of singular integral operators
with fixed singularities to Banach algebras of singular integral operators
on weighted Lebesgue spaces with slowly oscillating Muckenhoupt weights is
proved on the basis of Balakrishnans formula from the theory of strongly
continuous semi-groups of closed linear operators. Symbol calculus for such
operators, Fredholm criteria and index formulas are obtained. 相似文献
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In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem. Nonlinear term may be singular at t= 0 and/or t - 1 and x =0. 相似文献
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In this paper we consider oscillatory integral operators with strong singularities on . We obtain sharp decay estimates for L2 operator norm. We also obtain Hp estimates for difference of oscillatory strongly singular integral operators and strongly singular integral operators, which gives Lp mapping properties of oscillatory strongly singular integral operators. 相似文献
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兰家诚 《纯粹数学与应用数学》2004,20(4):317-322,326
通过相关的分数次积分算子的性质,证明了一类多线性算子在Hardy空间上的(Hp,Lp)有界性,得到一种简明的方法. 相似文献
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分析了二维问题边界元法3节点二次单元的几何特征,区分和定义了源点相对高阶单元的Ⅰ型和Ⅱ型接近度.针对二维位势问题高阶边界元中奇异积分核,构造出具有相同Ⅱ型几乎奇异性的近似核函数,在几乎奇异积分单元上分离出积分核中主导的奇异函数部分.原积分核扣除其近似核函数后消除几乎奇异性,成为正则积分核函数,并采用常规Gauss数值方法计算该正则积分;对奇异核函数的积分推导出解析公式,从而建立了一种新的边界元法高阶单元几乎奇异积分半解析算法.应用该算法计算了二维薄体结构温度场算例,计算结果表明高阶单元半解析算法能充分发挥边界元法优势,显著提高计算精度. 相似文献
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This paper gives a type theorem, which is a boundedness criterion for singular integral operators from the weighted Herz‐type Hardy spaces into the weighted local Herz‐type Hardy spaces. As applications, the corresponding mapping properties for the Cauchy integral and Calderón's commutators are obtained. In addition, a counter example is shown that neither is a Calderón–Zygmund singular integral operator bounded on the homogeneous local Herz‐type Hardy space, nor bounded on the classical local Hardy space. 相似文献