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Hausdorff dimension and σ finiteness of p harmonic measures in space when p ≥ n

Akman, Murat and Lewis, John and Vogel, Andrew (2015) 'Hausdorff dimension and σ finiteness of p harmonic measures in space when p ≥ n.' Nonlinear Analysis: Theory, Methods and Applications, 129. pp. 198-216. ISSN 0362-546X

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Abstract

In this paper we study a measure, μ associated with a positive p harmonic function û defined in an open set O⊂ℝR<sup>n</sup> and vanishing on a portion Γ of ∂O. If p>n we show μ is concentrated on a set of σ finite Hn-<sup>1</sup> measure while if p=n the same conclusion holds provided Γ is uniformly fat in the sense of n capacity. Our work nearly answers in the affirmative a conjecture in Lewis (2015) and also appears to be the natural extension of Jones and Wolff (1988), Wolff (1993), to higher dimensions.

Item Type: Article
Additional Information: owner: makman timestamp: 2012.02.13
Uncontrolled Keywords: p harmonic function; p Laplacian; p harmonic measure; Hausdorff measure
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 12 Sep 2019 15:46
Last Modified: 06 Jan 2022 14:01
URI: http://repository.essex.ac.uk/id/eprint/25313

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