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

Murat Akman, John Lewis, Andrew Vogel

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In this paper we study a measure, μ associated with a positive p harmonic function û defined in an open set O⊂ℝRn and vanishing on a portion Γ of ∂O. If p>n we show μ is concentrated on a set of σ finite Hn-1 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.

Original languageEnglish (US)
Pages (from-to)198-216
Number of pages19
JournalNonlinear Analysis, Theory, Methods and Applications
Volume129
DOIs
StatePublished - Dec 1 2015

Keywords

  • MSC primary 35J25
  • secondary 35J70

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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