Nonlocal isoperimetric inequalities for Kolmogorov-Fokker-Planck operators

被引：10
|
作者：
Garofalo, Nicola [1 ]
Tralli, Giulio [1 ]
机构：
[1] Univ Padua, Dipartimento Ingn Civile & Ambientale DICEA, Via Marzolo 9, Padua 35131, Italy
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 279卷 / 03期
关键词：
Kolmogorov operator; Non-symmetric semigroups; Nonlocal isoperimetric inequalities; SOBOLEV;
D O I：
10.1016/j.jfa.2020.108591
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we establish optimal isoperimetric inequalities for a nonlocal perimeter adapted to the fractional powers of a class of Kolmogorov-Fokker-Planck operators which are of interest in physics. These operators are very degenerate and do not possess a variational structure. The prototypical example was introduced by Kolmogorov in his 1938 paper on Brownian motion and the theory of gases. Our work has been influenced by ideas of M. Ledoux in the local case. (C) 2020 Elsevier Inc. All rights reserved.
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页数：40
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