二维Lipschitz区域上一类带L^p边值的非齐次多调和Neumann问题  

An L^p Inhomogeneous Polyharmonic Neumann Problem on Lipschitz Domains in R^2

作　　者：杜志华[1,2] 李玉妹 Du Zhihua;Li Yumei(Department of Mathematics,Jinan University,Guangzhou 510632;Faculty of Information Technology,Macao University of Science and Technology,Macao Taipa)

机构地区：[1]暨南大学数学系,广州510632 [2]澳门科技大学资讯科技学院,澳门氹仔

出　　处：《数学物理学报（A辑）》2020年第2期271-287,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11126065,11401254,11701597);澳门科技发展基金(MSAR.Ref.045/2015/A2)。

摘　　要：该文运用层位势方法研究了二维Lipschitz区域上一类带L^p边值的非齐次多调和Neumann问题.利用多层S位势,给出了该类问题的惟一积分表示解,其中,多层S位势是经典单层位势的高阶类似物,通过多调和基本解加以定义.In this paper,we study an inhomogeneous polyharmonic Neumann problem with L^p boundary data on Lipschitz domains in R^2 by the method of layer potentials.Applying multilayer S-potentials,which are higher order analogues of the classical singular layer potential and defined in terms of polyharmonic fundamental solutions,the unique integral representation solution is given for the inhomogeneous polyharmonic Neumann problem on Lipschitz domains in R^2 when the boundary data are in some L^p spaces.

关 键 词：多调和基本解 多层S位势 非齐次Neumann问题 多调和方程 

分 类 号：O175.8[理学—数学]