The Kusuoka measure and the energy Laplacian on level-$k$ Sierpiński gaskets
The Kusuoka measure and the energy Laplacian on level-$k$ Sierpiński gaskets
We extend and survey results in the theory of analysis on fractal sets from the standard Laplacian on the Sierpinski gasket to the energy Laplacian, which is defined weakly by using the Kusuoka energy measure. We also extend results from the Sierpinski gasket to level-$k$ Sierpinski gaskets, for all $k\geq …