Energy and Laplacian of Fractal Interpolation Functions

2016/07/21 by Xiaohui Li, Li, Xiao-Hui, Huo-Jun Ruan +1
Mathematics · Physics and Astronomy · #28A80 (Primary) #41A30 #47B39 (Secondary) #Advanced Mathematical Theories and Applications #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1607.06176

openalex publication_date 2016/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Sierpinski gasket (SG). As an application, we prove that the solution of the following Dirichlet problem on SG is an FIF with uniform vertical scaling factor (1)/(5): Δu=0 on SG∖ \q₁,q₂,q₃\, 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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