Kolmogorov-Fokker-Planck算子的非局部等周不等式
偏微分方程分析
2020-04-22 v3
摘要
在本文中，我们针对一类在物理学中引人关注的非局部周长，建立了适配于某类Kolmogorov-Fokker-Planck算子分数幂的最优等周不等式。这些算子高度退化且不具备变分结构。其原型例子由Kolmogorov在其1938年关于布朗运动与气体理论的论文中引入。我们的工作受到了M. Ledoux在局部情形中思想的启发。
引用
@article{arxiv.1907.02281,
title = {Nonlocal isoperimetric inequalities for Kolmogorov-Fokker-Planck operators},
author = {Nicola Garofalo and Giulio Tralli},
journal= {arXiv preprint arXiv:1907.02281},
year = {2020}
}
备注
The paper is going to appear in J. Funct. Anal. (doi.org/10.1016/j.jfa.2020.108591). With respect to a preliminary version, the content of Section 7 has been added