扇形域上高阶Schwarz边值问题（英文）  

HIGH ORDER SCHWARZ BOUNDARY VALUE PROBLEM IN A SECTOR

作　　者：王莹[1] 叶留青[2] 童丽珍[1] 

机构地区：[1]中南财经政法大学统计与数学学院,湖北武汉430073 [2]焦作师范高等专科学校数学系,河南焦作454002

出　　处：《数学杂志》2016年第1期1-5,共5页Journal of Mathematics

基　　金：Supported by Tianyuan Foundation of China(11326087);the Fundamental Research Funds for the Central Universities;the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry

摘　　要：本文主要讨论一类角度为θ=π/α,α≥1/2的扇形域上高阶多解析方程的Schwarz边值问题.通过构造适当的高阶-Schwarz算子和Pompeiu算子,我们给出了详细的解表达式.本文把边值问题进一步推广到高阶情形,丰富了扇形域上边值问题的发展.In this paper,we give a general discussion of Schwarz problem for polyanalytic equations in a sector with angle θ=π/α,a≥1/2.By constructing proper Poly-Schwarz and Pompeiu operators,the explicit solvability expressions for Schwarz problem are obtained,which extends the related result to higher order case and enriches the development of boundary problems in a sector.

关 键 词：Schwarz问题 高阶-Schwarz算子 Pompeiu算子 

分 类 号：O174.5[理学—数学] O175.8[理学—基础数学]