$(K_1, K_2)$-拟正则映射的 Hölder 连续性与几乎处处可微性
偏微分方程分析
2018-12-24 v3
摘要
本文研究 -拟正则映射。通过 Morrey 引理与等周不等式，证明了每一个 -拟正则映射在其定义域的紧子集上满足指数为 的 Hölder 条件，其中\n\begin{align} \alpha=\begin{cases} 1/K_1, & \text{for } K_1>1, \\ \text{any positive number less than } 1, & \text{for } K_1=1 \text{ and } K_2>0, \\ 1, & \text{for } K_1=1 \text{ and } K_2=0, \\ 1, & \text{for } K_1<1,\\ \end{cases} \end{align}\n并导出了 -拟正则映射的几乎处处可微性。
引用
@article{arxiv.1812.07779,
title = {H\"older Continuity and Differentiability Almost Everywhere of $(K_1, K_2)$-Quasiregular Mappings},
author = {Hongya Gao and Chao Liu and Junwei Li},
journal= {arXiv preprint arXiv:1812.07779},
year = {2018}
}
备注
This is an English version of our published Chinese article, available online at ( http://www.actamath.com/Jwk_sxxb_cn/CN/abstract/abstract21741.shtml ) and ( http://123.57.41.99/Jwk_sxxb_cn//CN/article/downloadArticleFile.do?attachType=PDF&id=21741 )