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. DOI https://doi.org/10.1016/j.na.2015.08.021
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. DOI https://doi.org/10.1016/j.na.2015.08.021
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. DOI https://doi.org/10.1016/j.na.2015.08.021
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 > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 12 Sep 2019 15:46 |
| Last Modified: | 30 Oct 2024 17:26 |
| URI: | http://repository.essex.ac.uk/id/eprint/25313 |
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Filename: 1306.5617v1.pdf