期刊
CHINESE ANNALS OF MATHEMATICS SERIES B
卷 36, 期 5, 页码 777-802出版社
SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
DOI: 10.1007/s11401-015-0976-7
关键词
Moser-Trudinger-Onofri inequality; Duality; Mass transportation; Fast diffusion equation; Rigidity
类别
资金
- STAB of the French National Research Agency (ANR)
- Kibord of the French National Research Agency (ANR)
- NoNAP of the French National Research Agency (ANR)
- ECOS [C11E07]
This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or the Onofri inequality for brevity. In dimension two this inequality plays a role similar to that of the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, the authors state several elementary remarks. Various new results are also proved in this paper. A proof of the inequality is given by using mass transportation methods (in the radial case), consistently with similar results for Sobolev inequalities. The authors investigate how duality can be used to improve the Onofri inequality, in connection with the logarithmic Hardy-Littlewood-Sobolev inequality. In the framework of fast diffusion equations, it is established that the inequality is an entropy-entropy production inequality, which provides an integral remainder term. Finally, a proof of the inequality based on rigidity methods is given and a related nonlinear flow is introduced.
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