Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities

S. Ibrahim, N. Masmoudi, K. Nakanishi, F. Sani

Research output: Contribution to journalArticlepeer-review


We study existence of maximizer for the Trudinger-Moser inequality with general nonlinearity of the critical growth on R2, as well as on the disk. We derive a very sharp threshold nonlinearity between the existence and the non-existence in each case, in asymptotic expansions with respect to growth and decay of the function. The expansions are explicit, using Apéry's constant. We also obtain an asymptotic expansion for the exponential radial Sobolev inequality on R2.

Original languageEnglish (US)
Article number108302
JournalJournal of Functional Analysis
Issue number1
StatePublished - Jan 1 2020


  • Concentration compactness
  • Maximizer
  • Sobolev critical exponent
  • Trudinger-Moser inequality

ASJC Scopus subject areas

  • Analysis


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