Energy and Laplacian of fractal interpolation functions

被引：1
|
作者：
Li Xiao-hui [1 ]
Ruan Huo-jun [1 ]
机构：
[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
来源：
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B | 2017年 / 32卷 / 02期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Dirichlet problem; fractal interpolation function; Sierpinski gasket; energy; Laplacian;
D O I：
10.1007/s11766-017-3482-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket (SG). As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5: Delta u = 0 on SG {q (1), q (2), q (3)}, and u(q (i) ) = a (i) , i = 1, 2, 3, where q (i) , i = 1, 2, 3, are boundary points of SG.
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页码：201 / 210
页数：10
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