Boundary value problems on part of a level-n Sierpinski gasket

Boundary value problems

Xuliang Li¹ 

[1] Department of Mathematical Sciences, Tsinghua University, Beijing, China

关键词: boundary value problems;    level-n Sierpinski gasket;    harmonic functions;    postcritically finite;    fractal Laplacian;    28A80;    35J25;   

DOI  :  10.1186/s13661-017-0781-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study the boundary value problems for the Laplacian on a sequence of domains constructed by cutting level-n Sierpinski gaskets properly. Under proper assumptions on these domains, we manage to give an explicit Poisson integral formula to obtain a series of solutions subject to the boundary data. In particular, it is proved that there exists a unique solution continuous on the closure of the domain for a given sequence of convergent boundary values.

【 授权许可】

CC BY