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dc.contributor.authorIbrahim, Slimja
dc.contributor.authorMasmoudi, Naderja
dc.contributor.authorNakanishi, Kenjija
dc.contributor.alternative中西, 賢次ja
dc.description.abstractTrudinger-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.ja
dc.publisherEMS Publishing Houseja
dc.rights© 2015 EMS Publishing House.ja
dc.rightsThis 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。ja
dc.subjectSobolev critical exponentja
dc.subjectTrudinger-Moser inequalityja
dc.subjectconcentration compactnessja
dc.subjectnonlinear Schr ödinger equationja
dc.subjectground stateja
dc.titleTrudinger–Moser inequality on the whole plane with the exact growth conditionja
dc.type.niitypeJournal Articleja
dc.identifier.jtitleJournal of the European Mathematical Societyja
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