Let (Formula presented.), (Formula presented.) and (Formula presented.). Our aim is to clarify the influence of the constraint (Formula presented.) on concentration phenomena of (spherically symmetric and non-increasing) maximizing sequences for the Trudinger–Moser supremum (Formula presented.) where (Formula presented.) is the sharp exponent of Moser, i.e. (Formula presented.) and (Formula presented.) is the surface measure of the (Formula presented.)-dimensional unit sphere in (Formula presented.). We obtain a vanishing-concentration-compactness alternative showing that maximizing sequences for (Formula presented.) cannot concentrate either when (Formula presented.) or when (Formula presented.) and (Formula presented.) is sufficiently small. From this alternative, we deduce the attainability of (Formula presented.) for special values of the parameters (Formula presented.) and (Formula presented.).

Vanishing-concentration-compactness alternative for the Trudinger-Moser inequality in R^N / J.M. Do Ó, F. Sani, C. Tarsi. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 20:1(2018 Feb 01).

Vanishing-concentration-compactness alternative for the Trudinger-Moser inequality in R^N

F. Sani
Penultimo
;
C. Tarsi
Ultimo
2018

Abstract

Let (Formula presented.), (Formula presented.) and (Formula presented.). Our aim is to clarify the influence of the constraint (Formula presented.) on concentration phenomena of (spherically symmetric and non-increasing) maximizing sequences for the Trudinger–Moser supremum (Formula presented.) where (Formula presented.) is the sharp exponent of Moser, i.e. (Formula presented.) and (Formula presented.) is the surface measure of the (Formula presented.)-dimensional unit sphere in (Formula presented.). We obtain a vanishing-concentration-compactness alternative showing that maximizing sequences for (Formula presented.) cannot concentrate either when (Formula presented.) or when (Formula presented.) and (Formula presented.) is sufficiently small. From this alternative, we deduce the attainability of (Formula presented.) for special values of the parameters (Formula presented.) and (Formula presented.).
Trudinger–Moser inequality; vanishing; concentration
Settore MAT/05 - Analisi Matematica
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/457285
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