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

By Nader Masmoudi, Federica Sani. 2015

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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 .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eb3a6d76321d95fa98c345752ea7640fe376c1b1