Trudinger-Moser Inequalities with the Exact Growth Condition in ℝN and Applications

Nader Masmoudi, Federica Sani

Research output: Contribution to journalArticlepeer-review


In a recent paper [19], the authors obtained a sharp version of the Trudinger-Moser inequality in the whole space ℝ2, giving necessary and sufficient conditions for the boundedness and the compactness of general nonlinear functionals in W 1, 2(ℝ2). We complete this study showing that an analogue of the result in [19] holds in arbitrary dimensions N ≥2. We also provide an application to the study of the existence of ground state solutions for quasilinear elliptic equations in ℝN.

Original languageEnglish (US)
Pages (from-to)1408-1440
Number of pages33
JournalCommunications in Partial Differential Equations
Issue number8
StatePublished - Aug 3 2015


  • Ground state solutions
  • Limiting Sobolev embeddings
  • Nonlinear Schrödinger equations
  • Trudinger-Moser inequalities

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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