BOUNDARY VALUE PROBLEMS FOR HARMONIC FUNCTIONS ON DOMAINS IN SIERPINSKI GASKETS

被引：2
|
作者：
Cao, Shiping [1 ]
Qiu, Hua [2 ]
机构：
[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA
[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 02期
关键词：
Boundary value problems; harmonic functions; fractal Laplacians; Sierpinski gasket; energy estimates; DIRICHLET FORMS; TRACE THEOREM;
D O I：
10.3934/cpaa.2020054
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study boundary value problems for harmonic functions on certain domains in the level-l Sierpinski gaskets SG(1) (l >= 2) whose boundaries are Cantor sets. We give explicit analogues of the Poisson integral formula to recover harmonic functions from their boundary values. Three types of domains, the left half domain of SG(1) and the upper and lower domains generated by horizontal cuts of SG(1) are considered at present. We characterize harmonic functions of finite energy and obtain their energy estimates in terms of their boundary values. This paper settles several open problems raised in previous work.
引用
收藏
页码：1147 / 1179
页数：33
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