亚椭圆算子的庞加莱不等式与定量De Giorgi方法
偏微分方程分析
2025-08-07 v3
摘要
我们提出了一种基于轨道的系统方法，用于证明具有任意数量Hörmander交换子的亚椭圆方程弱非负下解的庞加莱不等式，包括局部和非局部情形。作为推论，我们沿De Giorgi方法的思路推导出弱Harnack不等式和Hölder正则性。
引用
@article{arxiv.2401.12194,
title = {Poincar\'e inequality and quantitative De Giorgi method for hypoelliptic operators},
author = {Francesca Anceschi and Helge Dietert and Jessica Guerand and Amélie Loher and Clément Mouhot and Annalaura Rebucci},
journal= {arXiv preprint arXiv:2401.12194},
year = {2025}
}
备注
23 pages, 4 figures. Rewrote the introduction and clarified the ellipticity assumption