Murat Akman, John Lewis, Andrew Vogel
Published 2013-06-24Version 1
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.
On the dimension of a certain measure in the plane
$σ-$finiteness of a certain Borel measure associated with a positive weak solution to a quasilinear elliptic PDE in space
BMO solvability and absolute continuity of harmonic measure
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