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arXiv · 1306.5617

Hausdorff dimension and $\sigma$ finiteness of $p-$harmonic measures in space when $p\geq n$

Murat Akman·John Lewis·Andrew Vogel
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Abstract

In this paper we study a p harmonic measure, associated with a positive p harmonic function \hat{u} defined in an open set O, subset of R^n, and vanishing on a portion \Gamma of boundary of O. If p>n we show that this p harmonic measure is concentrated on a set of \sigma- finite H^{n-1} measure while if p=n the same conclusion holds provided \Gamma is uniformly fat in the sense of n capacity.

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Murat Akman, John Lewis, Andrew Vogel. 2013-06-24. Hausdorff dimension and $\sigma$ finiteness of $p-$harmonic measures in space when $p\geq n$. https://arxiv.org/abs/1306.5617

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