Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities

S. Ibrahim; N. Masmoudi; K. Nakanishi; F. Sani

doi:10.1016/j.jfa.2019.108302

Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities

S. Ibrahim, N. Masmoudi, K. Nakanishi, F. Sani

Research output: Contribution to journal › Article › peer-review

Abstract

We study existence of maximizer for the Trudinger-Moser inequality with general nonlinearity of the critical growth on R², as well as on the disk. We derive a very sharp threshold nonlinearity between the existence and the non-existence in each case, in asymptotic expansions with respect to growth and decay of the function. The expansions are explicit, using Apéry's constant. We also obtain an asymptotic expansion for the exponential radial Sobolev inequality on R².

Original language	English (US)
Article number	108302
Journal	Journal of Functional Analysis
Volume	278
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2019.108302
State	Published - Jan 1 2020

Keywords

Concentration compactness
Maximizer
Sobolev critical exponent
Trudinger-Moser inequality

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2019.108302

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title = "Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities",

abstract = "We study existence of maximizer for the Trudinger-Moser inequality with general nonlinearity of the critical growth on R2, as well as on the disk. We derive a very sharp threshold nonlinearity between the existence and the non-existence in each case, in asymptotic expansions with respect to growth and decay of the function. The expansions are explicit, using Ap{\'e}ry's constant. We also obtain an asymptotic expansion for the exponential radial Sobolev inequality on R2.",

keywords = "Concentration compactness, Maximizer, Sobolev critical exponent, Trudinger-Moser inequality",

author = "S. Ibrahim and N. Masmoudi and K. Nakanishi and F. Sani",

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AU - Ibrahim, S.

AU - Masmoudi, N.

AU - Nakanishi, K.

AU - Sani, F.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We study existence of maximizer for the Trudinger-Moser inequality with general nonlinearity of the critical growth on R2, as well as on the disk. We derive a very sharp threshold nonlinearity between the existence and the non-existence in each case, in asymptotic expansions with respect to growth and decay of the function. The expansions are explicit, using Apéry's constant. We also obtain an asymptotic expansion for the exponential radial Sobolev inequality on R2.

AB - We study existence of maximizer for the Trudinger-Moser inequality with general nonlinearity of the critical growth on R2, as well as on the disk. We derive a very sharp threshold nonlinearity between the existence and the non-existence in each case, in asymptotic expansions with respect to growth and decay of the function. The expansions are explicit, using Apéry's constant. We also obtain an asymptotic expansion for the exponential radial Sobolev inequality on R2.

KW - Concentration compactness

KW - Maximizer

KW - Sobolev critical exponent

KW - Trudinger-Moser inequality

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

M1 - 108302

ER -

Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities

Abstract

Keywords

ASJC Scopus subject areas

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