混合凸-凹边界对玻尔兹曼解正则性的影响
偏微分方程分析
2025-07-16 v2
摘要
域的几何性质是影响玻尔兹曼边界问题正则性的已知关键因素。在非凸物理边界存在时,已研究高度奇异行为,包括间断的传播\cite{Kim11}与H"older正则性\cite{CD2022}。本文我们聚焦于研究同心圆柱内玻尔兹曼方程的 H"older正则性,其边界同时呈现凸与凹特征。我们的发现推广了\cite{CD2022}的先前结果,该文主要处理凹性同时考虑凸物体外部。
引用
@article{arxiv.2311.10838,
title = {The Mixed Convex-Concave effect on the regularity of a Boltzmann solution},
author = {Gayoung An and Donghyun Lee},
journal= {arXiv preprint arXiv:2311.10838},
year = {2025}
}
备注
47 pages, 11 figures ; Remark 1.5 and 1.6 were added for Theorem 1.3. Some proofs have been shortened and simplified