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 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 {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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We are grateful to the referees for their helpful suggestions.
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Supported by the National Natural Science Foundation of China (11271327), and Zhejiang Provincial National Science Foundation of China (LR14A010001).
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Li, Xh., Ruan, Hj. Energy and Laplacian of fractal interpolation functions. Appl. Math. J. Chin. Univ. 32, 201–210 (2017). https://doi.org/10.1007/s11766-017-3482-8
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DOI: https://doi.org/10.1007/s11766-017-3482-8