We first investigate concentration and vanishing phenomena concerning Moser type inequalities in the whole plane which involve complete and reduced Sobolev norms. In particular we show that the critical Ruf inequality is equivalent to an improved version of the subcritical Adachi-Tanaka inequality which we prove to be attained. Then, we consider smooth compactly supported functions with respect to the Dirichlet norm parallel to Delta .parallel to(2), and we prove an optimal Lorentz-Zygmund type inequality with explicit extremals and from which can be derived classical inequalities in H-1(R-2) such as the Adachi-Tanaka inequality and a version of Ruf's inequality.

Equivalent Moser type inequalities in R^2 and the zero mass case / D. Cassani, F. Sani, C. Tarsi. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 267:11(2014), pp. 4236-4263. [10.1016/j.jfa.2014.09.022]

Equivalent Moser type inequalities in R^2 and the zero mass case

D. Cassani
Primo
;
F. Sani
Secondo
;
C. Tarsi
Ultimo
2014

Abstract

We first investigate concentration and vanishing phenomena concerning Moser type inequalities in the whole plane which involve complete and reduced Sobolev norms. In particular we show that the critical Ruf inequality is equivalent to an improved version of the subcritical Adachi-Tanaka inequality which we prove to be attained. Then, we consider smooth compactly supported functions with respect to the Dirichlet norm parallel to Delta .parallel to(2), and we prove an optimal Lorentz-Zygmund type inequality with explicit extremals and from which can be derived classical inequalities in H-1(R-2) such as the Adachi-Tanaka inequality and a version of Ruf's inequality.
Trudinger-Moser inequalities; Unbounded domains; Critical growth; Lorentz-Zygmund spaces; adams-type inequalities; Lorentz-Sobolev spaces; Klein-Gordon equation; R-N; unbounded-domains; trudinger inequalities; boundary-conditions; critical growth; ground-state; existence
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/251039
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