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Energy and Laplacian of fractal interpolation functions

被引：0
|
作者：
Xiao-hui Li
Huo-jun Ruan
机构：
[1] Zhejiang University,School of Mathematical Science
来源：
Applied Mathematics-A Journal of Chinese Universities | 2017年 / 32卷
关键词：
Dirichlet problem; fractal interpolation function; Sierpinski gasket; energy; Laplacian; Primary 28A80; Secondary 41A30; 47B39;
D O I：
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中图分类号：
学科分类号：
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: Δu = 0 on SG {q1, q2, q3}, and u(qi) = ai, i = 1, 2, 3, where qi, i = 1, 2, 3, are boundary points of SG.
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页码：201 / 210
页数：9
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