Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ<sup>N</sup> and Applications

Nader Masmoudi, Federica Sani

Research output: Contribution to journalArticle

Abstract

In a recent paper [19], the authors obtained a sharp version of the Trudinger-Moser inequality in the whole space ℝ<sup>2</sup>, giving necessary and sufficient conditions for the boundedness and the compactness of general nonlinear functionals in W <sup>1, 2</sup>(ℝ<sup>2</sup>). 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 ℝ<sup>N</sup>.

Original languageEnglish (US)
Pages (from-to)1408-1440
Number of pages33
JournalCommunications in Partial Differential Equations
Volume40
Issue number8
DOIs
StatePublished - Aug 3 2015

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Trudinger-Moser Inequality
Ground State Solution
Quasilinear Elliptic Equation
Growth Conditions
Ground state
Compactness
Boundedness
Analogue
Necessary Conditions
Sufficient Conditions
Arbitrary

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ<sup>N</sup> and Applications. / Masmoudi, Nader; Sani, Federica.

In: Communications in Partial Differential Equations, Vol. 40, No. 8, 03.08.2015, p. 1408-1440.

Research output: Contribution to journalArticle

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