非均匀调和函数的两类边值问题与积分表达式  

Two Kinds of Boundary Value Problems and Integral Expressions for Heterogeneous Harmonic Functions

作　　者：俞荣杰 郑允望 陶继成 YU Rongjie;ZHENG Yunwang;TAO Jicheng(School of Sciences, China Jiliang University, Hangzhou 310018, China)

机构地区：[1]中国计量大学理学院,浙江杭州310018

出　　处：《高等数学研究》2022年第1期41-48,73,共9页Studies in College Mathematics

基　　金：中国计量大学学生科研计划项目,2020年校级一流本科课程建设(200113).

摘　　要：本文给出非均匀指数函数的定义及性质,并且进一步引入了非均匀三角函数、非均匀双曲函数和非均匀对数函数.最后利用非均匀指数函数表达形式和非均匀解析函数的Cauchy积分理论,建立了非均匀泊松积分公式和非均匀施瓦茨积分公式,获得了非均匀调和函数在两类特殊边界上的狄利克雷问题和诺伊曼问题解的显示表达式.In this paper,the definition and properties of heterogeneous exponential function are given,and heterogeneous trigonometric function,heterogeneous hyperbolic function and heterogeneous logarithmic function are introduced.Using the heterogeneous exponential function and heterogeneous Cauchy integral theory of heterogeneous analytic function,heterogeneous Poisson integral formula and heterogeneous Schwaz integral formula are established,the explicit expressions of the Dirichlet problem and the Neumann problem of the heterogeneous harmonic functions on the special boundary conditions are obtained.

关 键 词：非均匀调和函数 非均匀狄利克雷问题 非均匀诺伊曼问题 积分核 

分 类 号：O174.5[理学—数学]