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>.
Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ<sup>N</sup> and Applications / N. Masmoudi, F. Sani. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 40:8(2015 Aug 03), pp. 1408-1440. [10.1080/03605302.2015.1026775]
Trudinger-Moser Inequalities with the Exact Growth Condition in ℝN and Applications
F. Sani
2015
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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