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On the absolute continuity of p-harmonic measure and surface measure in Reifenberg flat domains

Akman, Murat (2016) 'On the absolute continuity of p-harmonic measure and surface measure in Reifenberg flat domains.' Pacific Journal of Mathematics, 286 (1). pp. 25-37. ISSN 0030-8730

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Abstract

We study the set of absolute continuity of p-harmonic measure μ associated to a positive weak solution to the p-Laplace equation with continuous zero boundary values and.n-1/-dimensional Hausdorffmeasure n-1 on locally flat domains in space. We prove that when n ≥ 2 and 2 < p < ∞ and when n ≥ 3 and 2-η < p < 2 for some η > 0 there exist locally flat domains Ω ⊂ ℝn with locally finite perimeter and Borel sets E ⊂ ∂Ω such that μ(E) > 0 = n-1(E).

Item Type: Article
Additional Information: 13 pages, some minor changes
Uncontrolled Keywords: math.AP; 35J25, 37F35, 31A15, 28A75, 28A78
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 25 Jul 2019 13:55
Last Modified: 06 Jan 2022 14:01
URI: http://repository.essex.ac.uk/id/eprint/25001

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