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arXiv · 1212.0148

Energy Measures of Harmonic Functions on the Sierpi\'nski Gasket

Renee Bell·Ching-Wei Ho·Robert S. Strichartz
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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 $V_*$ 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.

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Renee Bell, Ching-Wei Ho, Robert S. Strichartz. 2012-12-01. Energy Measures of Harmonic Functions on the Sierpi\'nski Gasket. https://arxiv.org/abs/1212.0148

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