Several logarithmic Caffarelli-Kohn-Nirenberg inequalities and applications

被引：3
|
作者：
Feng, Tingfu [1 ]
Niu, Pengcheng [1 ]
Qiao, Jing [1 ]
机构：
[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 457卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Logarithmic; Caffarelli-Kohn-Nirenberg inequality; Parameter type logarithmic Caffarelli-Kohn-Nirenberg inequality; The Heisenberg group; Generalized Baouendi-Grushin vector fields; ELLIPTIC-EQUATIONS; EXTREMAL-FUNCTIONS; GRUSHIN; NONEXISTENCE; EXISTENCE; CONSTANTS; SYMMETRY;
D O I：
10.1016/j.jmaa.2017.08.042
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, based on the Caffarelli-Kohn-Nirenberg inequalities on the Euclidean space and the weighted Holder inequality, we establish the logarithmic Caffarelli-Kohn-Nirenberg inequalities and parameter type logarithmic Caffarelli-Kohn-Nirenberg inequalities, and give applications for the weighted ultracontractivity of positive strong solutions to a kind of evolution equations. We also prove corresponding logarithmic Caffarelli-Kohn-Nirenberg inequalities and parameter type logarithmic Caffarelli-Kohn-Nirenberg inequalities on the Heisenberg group and related to generalized Baouendi-Grushin vector fields. Some applications are provided. (c) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：822 / 840
页数：19
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