非齐次Moisil-Theodorsco方程组的Riemann边值问题  

The Riemann Boundary Value Problem in Inhomogeneous Moisil-Theodorsco System

作　　者：李觉友[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2007年第4期26-29,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10671207)

摘　　要：考虑了在R3空间中的非齐次Moisil-Theodorsco方程组的Riemann边值问题。本文首先研究Moisil-Theodor-sco方程组的Cauchy型积分,Plemelj公式,进而得到了非齐次Moisil-Theodorsco方程组解的积分表示和它的Plemelj公式,在此基础上还讨论了它的一个Riemann边值问题。最后运用积分方程方法和Banach不动点定理证明了该Ri-emann边值问题解的存在性和唯一性,同时也给出了其解的积分表示式。It is well known that function theory methods becomes, in recent years, a powerfull mathematical tool for the treatment of boundary value problems which have a lots of application in mathematical physics and engineering in domains over Eulidean spaces of higher dimension. In this paper, the Riemann boundary value problem is investigated in inhomogeneous Moisil-Theodorsco system 偏d F =f in the D which is a bounded domain of R^3 with smooth or piece smooth boundary Г. Found is a solution F（η） of equation OF =f in the D, which is continuous in ^-D and satisfying the Riemann boundary condition F^＋ （η） = G（η）F^- （η） ＋ g（η） ,η∈ Г where G（η） ,g（η）∈H（Г,β） are given complex value function on Г. To deal with the Riemann boundary value problem, first of all, we study some properties of the Cauchy type integral and the Plemelj formula in Moisil-Theodorsco system, and then give the Plemelj formula and the integral expression of the solution in inhomogeneous Moisil-Theodorsco system. Secondly, we estimate the singular integral operator K understood in the sense of Cauchy principal value, which is a bounded linear operator mapping from the function space H（Г,β） into itself. Finally, we apply the method of integral equations and Banach fixed point theorem, existence and uniqueness of the solution for the above mentioned boundary value problem have already proved. At the same time, the precisely integral expression of its solution is also obrained.

关 键 词：Moisil-Theodorsco方程组 PLEMELJ公式 RIEMANN边值问题 

分 类 号：O175.5[理学—数学]