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

Nader Masmoudi; Federica Sani

doi:10.1080/03605302.2015.1026775

Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ^N and Applications

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Abstract

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 ℝ^N.

Original language	English (US)
Pages (from-to)	1408-1440
Number of pages	33
Journal	Communications in Partial Differential Equations
Volume	40
Issue number	8
DOIs	https://doi.org/10.1080/03605302.2015.1026775
State	Published - Aug 3 2015

Keywords

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

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1080/03605302.2015.1026775

Cite this

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abstract = "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.",

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AB - 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.

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