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

被引：3

作者：

Akman, Murat ^{[1
]}

Lewis, John ^{[2
]}

Vogel, Andrew ^{[3
]}

机构：

[1] CSIC, Inst Ciencias Matemat CSIC UAM UC3M UCM, E-28049 Madrid, Spain

[2] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

[3] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 129卷

基金：

美国国家科学基金会;

关键词：

p harmonic function; p Laplacian; p harmonic measure; Hausdorff measure; SETS;

D O I：

10.1016/j.na.2015.08.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a measure, it, associated with a positive p harmonic function (u) over cap defined in an open set O subset of R-n and vanishing on a portion Gamma of partial derivative O. If p > n we show it is concentrated on a set of sigma finite Hn-1 measure while if p = n the same conclusion holds provided Gamma 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. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：198 / 216

页数：19

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