A sharpened Moser-Pohozaev-Trudinger inequality with mean value zero in \(\mathbb R^2\)
type: Item
instance of: scholarly article
title: A sharpened Moser-Pohozaev-Trudinger inequality with mean value zero in \(\mathbb R^2\)
zbMATH Open document ID: 1179.58010
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-05-12T00:00:00Z
review text: From the abstract: Let \(\Omega \subset \mathbb{R}^2\) be a smooth bounded domain, and \(q(x)\) be a polynomial with \(q(0) \neq 0\). Then under some hypothesis on \(q(x)\), there holds \[ \sup_{\int_{\Omega} |\nabla u|^2\mathrm{d}x=1,\,\int_{\Omega}u\mathrm{d}x =0} \int_{\Omega} \mathrm{e}^{\frac{2\pi u^2}{q(0)}q(\int_{\Omega}u^2\mathrm{d}x) }\mathrm{d}x < \infty. \] A sufficient condition will be given to assure that the above inequality does not hold. Furthermore, the existence of the extremal functions will be derived.
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 5553053
zbMATH Keywords: Moser-Trudinger inequality
zbMATH Keywords: blowing up analysis
zbMATH Keywords: extremal function
author: Guozhen Lu
author: Yunyan Yang
MaRDI profile type: Publication
full work available at URL: j.na.2008.12.022
OpenAlex ID: W2037055151
cites work: Conformal deformations of metric on \({\mathcal S}\) 2
cites work: Q5547919
cites work: Q5603485
cites work: Blow-up Analysis in Dimension 2 and a Sharp Form of Trudinger–Moser Inequality
cites work: Q3756181
cites work: Extremal functions for the Trudinger-Moser inequality in 2 dimensions
cites work: Extremal functions for Moser’s inequality
cites work: Moser-Trudinger inequality on compact Riemannian manifolds of dimension two
cites work: Adams' inequalities for bi-Laplacian and extremal functions in dimension four
cites work: The concentration-compactness principle in the calculus of variations. The limit case. I
cites work: Elliptic partial differential equations of second order
cites work: Classification of solutions of some nonlinear elliptic equations
cites work: A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface
cites work: EXTREMAL FUNCTIONS FOR MOSER–TRUDINGER INEQUALITIES ON 2-DIMENSIONAL COMPACT RIEMANNIAN MANIFOLDS WITH BOUNDARY
cites work: Symmetry Theorems Related to Pompeiu's Problem
cites work: A sharp inequality of J. Moser for higher order derivatives
cites work: The inequality of Moser and Trudinger and applications to conformal geometry
DOI: 10.1016/J.NA.2008.12.022
description: scientific article; zbMATH DE number 5553053