Hausdorff dimension and $\sigma$ finiteness of $p-$harmonic measures in space when $p\geq n$
Murat Akman, John L. Lewis, Andrew L. Vogel · arXiv (Cornell University) · 2013
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.