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1.
The Poincaré-Bertrand formula and the composition formula for the Bochner-Martinelli integral on piecewise smooth manifolds
are obtained. As an application, the regularization problem for linear singular integral equation with Bochner-Martinelli
kernel and variable coefficients is discussed. 相似文献
2.
1 IntroductionSillce tl1e limit value fOrlnula, viz. tl1e Plemelj fOrn1ula, of the Cauthe type integraJ withBochner-Martinelli kernel was proved in 1957[1], it has beell successfully used to the study Ofsingular i1ltegral equatious, solvi11g the 0b--equation, holomorphic extension, 0--closed exten-sion and C-R 111al1ifolds[2-51. Evideutly, the researcl1 of higher order singular integrals withBochuer-Martinelli kerllel itself also l1as important significallce. In 1952, J. Hadanmrd firstde… 相似文献
3.
利用积分变换技巧,作者给出了C~n中闭光滑可定向流形上一个新的Bochner-Martinelli型积分的高阶偏导数的奇异积分的Hadamard主值,获得了高阶奇异积分的Plemelj公式和合成公式,还讨论了相应的变系数线性微分积分方程的正则化,证明其可转化为一类等价的Fredholm方程。并且指出其特征方程当给出一组适当的边值条件时,在L~*中存在唯一解。 相似文献
4.
Lü Tao 《Journal of Mathematical Analysis and Applications》2006,324(1):225-237
Based on a new generalization of discrete Gronwall inequality in [L. Tao, H. Yong, A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equality of the second kind, J. Math. Anal. Appl. 282 (2003) 56-62], Navot's quadrature rule for computing integrals with the end point singularity in [I. Navot, A further extension of Euler-Maclaurin summation formula, J. Math. Phys. 41 (1962) 155-184] and a transformation in [P. Baratella, A. Palamara Orsi, A new approach to the numerical solution of weakly singular Volterra integral equations, J. Comput. Appl. Math. 163 (2004) 401-418], a new quadrature method for solving nonlinear weakly singular Volterra integral equations of the second kind is presented. The convergence of the approximation solution and the asymptotic expansion of the error are proved, so by means of the extrapolation technique we not only obtain a higher accuracy order of the approximation but also get a posteriori estimate of the error. 相似文献
5.
Robert Aebi 《Probability Theory and Related Fields》1993,96(1):107-121
Summary Schrödinger equations are equivalent to pairs of mutually time-reversed non-linear diffusion equations. Here the associated diffusion processes with singular drift are constructed under assumptions adopted from the theory of Schrödinger operators, expressed in terms of a local space-time Sobolev space.By means of Nagasawa's multiplicative functionalN
s
t
, a Radon-Nikodym derivative on the space of continuous paths, a transformed process is obtained from Wiener measure. Its singular drift is identified by Maruyama's drift transformation. For this a version of Itô's formula for continuous space-time functions with first and second order derivatives in the sense of distributions satisfying local integrability conditions has to be derived.The equivalence is shown between weak solutions of a diffusion equation with singular creation and killing term and the solutions of a Feynman-Kac integral equation with a locally integrable potential function. 相似文献
6.
讨论了实 Clifford分析中的一类高阶奇异积分 ,给出了这类高阶奇异积分的递推公式 ,计算公式 ,并且研究了这类高阶奇异积分的 Hlder连续性 ,从而使实 Clifford分析理论得以拓展 . 相似文献
7.
This paper deals with the boundary value properties and the higher order singular integro-differential equation. On Stein
manifolds, the Hadamard principal value, the Plemelj formula and the composite formula for higher order Bochner–Martinelli
type integral are given. As an application, the composite formula is used for discussing the solution of the higher order
singular integro-differential equation. 相似文献
8.
Ding-dong Gong 《高校应用数学学报(英文版)》2008,23(3):273-278
Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well. 相似文献
9.
讨论了实Clifford分析中的一类高阶奇异积分,给出了这类高阶奇异积分的递推公式,计算公式.从而使实Clifford分析理论得以拓展. 相似文献
10.
Moulay Youssef Barkatou 《Journal of Geometric Analysis》2000,10(2):219-241
In this paper a new explicit integral formula is derived for solutions of the tangential Cauchy-Riemann equations on CR q-concave
manifolds and optimal estimates in the Lipschitz norms are obtained. 相似文献
11.
A method of explicit factorization of matrix functions of second order is proposed. The method consists of reduction of this problem to two scalar barrier problems and a finite system of linear equations. Applications to various classes of singular integral equations and equations with Toeplitz and Hankel matrices are given. 相似文献
12.
Solution of nonlinear weakly singular Volterra integral equations using the fractional‐order Legendre functions and pseudospectral method 下载免费PDF全文
Jafar Eshaghi Hojatollah Adibi Saeed Kazem 《Mathematical Methods in the Applied Sciences》2016,39(12):3411-3425
In this article, our main goal is to render an idea to convert a nonlinear weakly singular Volterra integral equation to a non‐singular one by new fractional‐order Legendre functions. The fractional‐order Legendre functions are generated by change of variable on well‐known shifted Legendre polynomials. We consider a general form of singular Volterra integral equation of the second kind. Then the fractional Legendre–Gauss–Lobatto quadratures formula eliminates the singularity of the kernel of the integral equation. Finally, the Legendre pseudospectral method reduces the solution of this problem to the solution of a system of algebraic equations. This method also can be utilized on fractional differential equations as well. The comparison of results of the presented method and other numerical solutions shows the efficiency and accuracy of this method. Also, the obtained maximum error between the results and exact solutions shows that using the present method leads to accurate results and fast convergence for solving nonlinear weakly singular Volterra integral equations. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
13.
SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER 总被引:1,自引:0,他引:1
钟寿国 《数学物理学报(B辑英文版)》2005,25(2):193-200
In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given. 相似文献
14.
In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points. 相似文献
15.
Ricardo Abreu-Blaya Juan Bory-Reyes Michael Shapiro 《Complex Analysis and Operator Theory》2007,1(2):143-168
In this paper we discuss the notion of the Bochner–Martinelli kernel for domains with rectifiable boundary in
, by expressing the kernel in terms of the exterior normal due to Federer (see [17,18]). We shall use the above mentioned
kernel in order to prove both Sokhotski–Plemelj and Plemelj–Privalov theorems for the corresponding Bochner–Martinelli integral,
as well as a criterion of the holomorphic extendibility in terms of the representation with Bochner–Martinelli kernel of a
continuous function of two complex variables.
Explicit formula for the square of the Bochner–Martinelli integral is rediscovered for more general surfaces of integration
extending the formula established first by Vasilevski and Shapiro in 1989.
The proofs of all these facts are based on an intimate relation between holomorphic function theory of two complex variables
and some version of quaternionic analysis.
Submitted: September 6, 2006. Accepted: November 1, 2006. 相似文献
16.
Chen Lüping 《数学物理学报(B辑英文版)》2006,26(4):679-690
Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C(1) smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation. 相似文献
17.
M. E. Abramyan 《Russian Mathematics (Iz VUZ)》2012,56(2):1-9
We study an approximate method for solving singular integral equations. It implies an approximation of a singular operator
by means of a compound quadrature formula similar to the rectangle one. The corresponding systems of linear algebraic equations
are solvable if so is the integral equation, while its coefficients satisfy the strong ellipticity condition. Under these
restrictions we obtain a bound for the rate of convergence of solutions of systems of linear equations to the solution of
the considered integral equation in the uniform vector norm. 相似文献
18.
Summary This paper deals with the question of the attainable order of convergence in the numerical solution of Volterra and Abel integral equations by collocation methods in certain piecewise polynomial spaces and which are based on suitable interpolatory quadrature for the resulting moment integrals. The use of a (nonlinear) variation of constants formula for the representation of the error function in terms of the defect allows for a unified treatment of equations with continuous and weakly singular kernels. 相似文献
19.
In this paper, we obtain the general permutation formulas and composition formulas of singular integral of the Bochner-Martinelli type on a closed piecewiseC
(1) smooth manifold. As an application, we consider the corresponding singular integral equation of linear variable coefficients, and prove that the singular integral equation can be transformed to an equivalent Fredholm equation, whose characteristic equation has a unique solution in
, here
denotes the function set which satisfies the Hölder condition on D and holomorphically expands to domainD.Corresponding author. Project supported in part by the Mathematical Tian Yuan Foundation of China (Grant No. TY10126033). 相似文献
20.
实Clifford分析中三类高阶奇异积分及其非线性微分积分方程 总被引:9,自引:0,他引:9
本文第一部分借助于高阶异积分的Hadamard主值的思想以及归纳法的思想,在证明了6个引理的基础上讨论实Clifford分析中三类高阶异积分的归纳定义,Hadamard主值的存在性,递推公式,计算公式以及高阶奇异积分在Hadamard主值意义下的12个微分公式,受多复变中解析函数积分表示式多样笥的,本文采用的算子的积分表达式就与个公式和微分公式都十分乘法本文第二部分在引进并证明了Hile引理型的基 相似文献