双侧NTA域上调和测度的单相问题
经典分析与常微分方程
2017-06-14 v2 偏微分方程分析
摘要
我们证明，若 是一个具有 AD-正则边界的双侧 NTA 域，且泊松核的对数属于 （其中 为 的表面测度），则 的外单位法向量也属于 。对于维数大于 的情形，类似结果不成立。这回答了 Kenig 与 Toro 以及 Bortz 与 Hofmann 提出的一个问题。
引用
@article{arxiv.1604.06343,
title = {The one-phase problem for harmonic measure in two-sided NTA domains},
author = {Jonas Azzam and Mihalis Mourgoglou and Xavier Tolsa},
journal= {arXiv preprint arXiv:1604.06343},
year = {2017}
}
备注
In this version we have corrected minor typos, and also we have cited correctly some previous work by Kenig and Toro, of which we were not aware before