Rearrangement and the weighted logarithmic Sobolev inequality

• 作者: JIANG Ming-hong RUAN Jian-miao ZHU Xiang-rong
• 来源期刊: 高校应用数学学报B辑（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 207-217
• 页数: 11页
• 语种: 英文
• DOI: 10.3969/j.issn.1005-1031.2021.02.004

摘要

Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemannian manifolds.We give the necessary and sufficient conditions such that the 1-dimension weighted logarithmic Sobolev inequality is true and obtain a new estimate on the entropy.