THE HARNACK INEQUALITY FOR SECOND-ORDER ELLIPTIC EQUATIONS WITH DIVERGENCE-FREE DRIFTS

被引：12
|
作者：
Ignatova, Mihaela [1 ]
Kukavica, Igor [2 ]
Ryzhik, Lenya [1 ]
机构：
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
[2] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA
来源：
COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2014年 / 12卷 / 04期
基金：
美国国家科学基金会;
关键词：
Harnack inequality; Liouville theorem; regularity; drift-diffusion equations; DIFFUSION;
D O I：
10.4310/CMS.2014.v12.n4.a4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b is an element of Ln/2+delta where delta > 0. As an application we provide a one-sided Liouville's theorem provided that b is an element of Ln/2+delta (R-n).
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页码：681 / 694
页数：14
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