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| The Moser-Trudinger-Onofri Inequality |
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Citation： |
Jean DOLBEAULT,Maria J. ESTEBAN,Gaspard JANKOWIAK.The Moser-Trudinger-Onofri Inequality[J].Chinese Annals of Mathematics B,2015,36(5):777~802 |
| Page view： 1187
Net amount： 1031 |
Authors： |
Jean DOLBEAULT; Maria J. ESTEBAN;Gaspard JANKOWIAK |
Foundation： |
This work was supported by the Projects STAB and Kibord
of the French National Research Agency (ANR), the Project NoNAP of
the French National Research Agency (ANR) and the ECOS Project
(No. C11E07). |
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| Abstract： |
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. |
Keywords： |
Moser-Trudinger-Onofri inequality, Duality, Mass transportation,
Fast diffusion equation, Rigidity |
Classification： |
26D10, 46E35, 35K55, 58J60 |
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