Hausdorff dimension and σ finiteness of p-harmonic measures in space when p≥ n
Abstract
In this paper we study a p harmonic measure, associated with a positive p harmonic function u defined in an open set O, subset of Rn, and vanishing on a portion of boundary of O. If p>n we show that this p harmonic measure is concentrated on a set of σ- finite Hn-1 measure while if p=n the same conclusion holds provided is uniformly fat in the sense of n capacity.
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