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Title: Trudinger–Moser inequality on the whole plane with the exact growth condition
Authors: Ibrahim, Slim
Masmoudi, Nader
Nakanishi, Kenji  kyouindb  KAKEN_id  orcid (unconfirmed)
Author's alias: 中西, 賢次
Keywords: Sobolev critical exponent
Trudinger-Moser inequality
concentration compactness
nonlinear Schr ödinger equation
ground state
Issue Date: 2015
Publisher: EMS Publishing House
Journal title: Journal of the European Mathematical Society
Volume: 17
Issue: 4
Start page: 819
End page: 835
Abstract: Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to L∞. It is well known that the original form of the inequality with the sharp exponent (proved by Moser) fails on the whole plane, but a few modi ed versions are available. We prove a precised version of the latter, giving necessary and sufficient conditions for the boundedness, as well as for the compactness, in terms of the growth and decay of the nonlinear function. It is tightly related to the ground state of the nonlinear Schr ödinger equation (or the nonlinear Klein-Gordon equation), for which the range of the time phase (or the mass constant) as well as the energy is given by the best constant of the inequality.
Rights: © 2015 EMS Publishing House.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
DOI(Published Version): 10.4171/JEMS/519
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