Energy Measures of Harmonic Functions on the Sierpi\'nski Gasket
Analysis of PDEs
2013-09-25 v3
Abstract
We study energy measures on SG based on harmonic functions. We characterize the positive energy measures through studying the bounds of Radon-Nikodym derivatives with respect to the Kusuoka measure. We prove a limited continuity of the derivative on the graph and express the average value of the derivative on a whole cell as a weighted average of the values on the boundary vertices. We also prove some characterizations and properties of the weights.
Keywords
Cite
@article{arxiv.1212.0148,
title = {Energy Measures of Harmonic Functions on the Sierpi\'nski Gasket},
author = {Renee Bell and Ching-Wei Ho and Robert S. Strichartz},
journal= {arXiv preprint arXiv:1212.0148},
year = {2013}
}