Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift

被引：14
|
作者：
Maekawa, Yasunori [1 ]
Miura, Hideyuki [2 ]
机构：
[1] Kobe Univ, Grad Sch Sci, Dept Math, Kobe, Hyogo 6578501, Japan
[2] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 264卷 / 10期
关键词：
Non-local diffusion; Divergence free drift; Fundamental solutions; Pointwise upper bound; GLOBAL WELL-POSEDNESS; INEQUALITIES;
D O I：
10.1016/j.jfa.2013.02.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider some non-local diffusion equations in the presence of a divergence free drift term, where the diffusion operators are related to certain Dirichlet forms of jump type. We derive pointwise upper bounds for fundamental solutions of the equations under weak assumptions for the velocity of the drift term. Our class of the velocity includes functions with the scale-critical regularity and some growing functions at spatial infinity. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：2245 / 2268
页数：24
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