二维Lipschitz区域上一类带Lp

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 271-287.

二维Lipschitz区域上一类带L^p

杜志华^1,^2,*(),李玉妹¹

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

收稿日期:2018-11-26 出版日期:2020-04-26 发布日期:2020-05-21
通讯作者: 杜志华 E-mail:tzhdu@jnu.edu.cn; zhdu@must.edu.mo
基金资助:
国家自然科学基金(11126065);国家自然科学基金(11401254);国家自然科学基金(11701597);澳门科技发展基金(MSAR.Ref.045/2015/A2)

An L^p Inhomogeneous Polyharmonic Neumann Problem on Lipschitz Domains in $\mathbb{R} ^{2}$

Zhihua Du^1,^2,*(),Yumei Li¹

¹ Department of Mathematics, Jinan University, Guangzhou 510632
² Faculty of Information Technology, Macau University of Science and Technology, Macao Taipa

Received:2018-11-26 Online:2020-04-26 Published:2020-05-21
Contact: Zhihua Du E-mail:tzhdu@jnu.edu.cn; zhdu@must.edu.mo
Supported by:
the NSFC(11126065);the NSFC(11401254);the NSFC(11701597);the Macao Science and Technology Development Fund(MSAR.Ref.045/2015/A2)

摘要/Abstract

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${\cal S}$位势,给出了该类问题的惟一积分表示解,其中,多层${\cal S}$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.

关键词: 多调和基本解, 多层${\cal S}$位势, 非齐次Neumann问题, 多调和方程

Abstract:

In this paper, we study an inhomogeneous polyharmonic Neumann problem with $L^{p}$ boundary data on Lipschitz domains in $\mathbb{R} ^{2}$ by the method of layer potentials. Applying multi-layer ${\cal S}$-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 $\mathbb{R} ^{2}$ when the boundary data are in some $L^{p}$ spaces.

Key words: Polyharmonic fundamental solutions, Multi-layer ${\cal S}$-potentials, Inhomogeneous Neumann problem, Polyharmonic equation

中图分类号:

O175.8

杜志华,李玉妹. 二维Lipschitz区域上一类带L^p[J]. 数学物理学报, 2020, 40(2): 271-287.

Zhihua Du,Yumei Li. An L^p Inhomogeneous Polyharmonic Neumann Problem on Lipschitz Domains in $\mathbb{R} ^{2}$[J]. Acta mathematica scientia,Series A, 2020, 40(2): 271-287.

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