Rearrangement and the weighted logarithmic Sobolev inequality

Rearrangement and the weighted logarithmic Sobolev inequality

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.

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Veröffentlicht in:Applied Mathematics-A Journal of Chinese Universities 2021-02, Vol.36 (2), p.207-217
Hauptverfasser: Jiang, Ming-hong, Ruan, Jian-miao, Zhu, Xiang-rong
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Riemann manifold
Theorems
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Zusammenfassung: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.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-021-3755-z