Rearrangement and the weighted logarithmic Sobolev inequality |
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| Authors: | JIANG Ming-hong RUAN Jian-miao ZHU Xiang-rong |
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| Affiliation: | Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China;Department of Mathematics,Zhejiang International Studies University,Hangzhou 310014,China |
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| Abstract: | 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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