Energy and Laplacian of Fractal Interpolation Functions
classification
🧮 math.FA
keywords
fifsfractalfunctionsinterpolationlaplacianscalinguniformvertical
pith:HSZ4LZ3V Add to your LaTeX paper
What is a Pith Number?\usepackage{pith}
\pithnumber{HSZ4LZ3V}
Prints a linked pith:HSZ4LZ3V badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more
read the original 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 $\frac{1}{5}$: $\Delta u=0$ on $SG\setminus \{q_1,q_2,q_3\}$, and $u(q_i)=a_i$, $i=1,2,3$, where $q_i$, $i=1,2,3$, are boundary points of SG.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.