Logarithmic Holder Estimates of p-Harmonic Extension Operators in a Metric Measure Space

被引：0

作者：

Itoh, Tsubasa ^{[1
]}

机构：

[1] Hokkaido Univ, Dept Math, Kita Ku, Sapporo, Hokkaido 0600810, Japan

来源：

COMPLEX ANALYSIS AND POTENTIAL THEORY | 2012年 / 55卷

关键词：

Modulus of continuity; p-harmonic; p-Dirichlet solution; metric measure space; p-capacity;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let 1 < p < infinity and let X be a metric measure space with a doubling measure and a (1, p)-Poincare inequality. Let Omega be a bounded domain in X. For a function f on partial derivative Omega we denote by P(Omega)f the p-harmonic extension of f over Omega. It is well known that if Omega is p-regular and f is an element of (partial derivative Omega), then P(Omega)f is continuous in (Omega) over bar. We characterize the family of domains such that logarithmic Holder continuity of boundary functions f ensures logarithmic Holder continuity of P(Omega)f.

引用

页码：163 / 169

页数：7