Non-existence of extremals for the Adimurthi-Druet inequality

DOI10.1016/j.jde.2018.07.065zbMath1417.35036arXiv1711.05022OpenAlexW2768553357WikidataQ129432053 ScholiaQ129432053MaRDI QIDQ1627692

Pierre-Damien Thizy, Gabriele Mancini

Publication date: 3 December 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.05022

zbMATH Keywords

extremal functionsDirichlet energyMoser-Trudinger inequalityAdimurthi-Druet inequality

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Semilinear elliptic equations (35J61)

Related Items (16)

Nonexistence of extremals for a Trudinger-Moser inequality on a Riemann surface with boundary ⋮ A remark on energy estimates concerning extremals for Trudinger-Moser inequalities on a disc ⋮ The nonexistence of extremals for the Hardy-Trudinger-Moser inequality in the hyperbolic space ⋮ On nonexistence of extremals for the Trudinger-Moser functionals involving \(L^p\) norms ⋮ Maximization problem on Trudinger-Moser inequality involving Lebesgue norm ⋮ Nonexistence of extremals for an inequality of Adimurthi-Druet on a closed Riemann surface ⋮ Energy estimates on existence of extremals for Trudinger-Moser inequalities ⋮ Extremal sections for a Trudinger-Moser functional on vector bundle over a closed Riemann surface ⋮ Glueing a peak to a non-zero limiting profile for a critical Moser-Trudinger equation ⋮ Supercritical Moser-Trudinger inequalities and related elliptic problems ⋮ A Trudinger-Moser inequality of Adimurthi-Druet type involving higher order eigenvalues ⋮ A supercritical Sobolev type inequality in higher order Sobolev spaces and related higher order elliptic problems ⋮ A remark on an improved Trudinger–Moser inequality in high dimensions ⋮ Existence of extremals for critical Trudinger-Moser inequalities via the method of energy estimate ⋮ Improved singular Moser-Trudinger inequalities and their extremal functions ⋮ Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities

Cites Work

• Unnamed Item
• Existence and nonexistence of maximizers for variational problems associated with Trudinger--Moser type inequalities in \({\mathbb{R}^N}\)
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• A sharp form of Moser-Trudinger inequality in high dimension
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Sharp constant and extremal function for the improved Moser-Trudinger inequality involving \(L^p\) norm in two dimension
• New solutions for Trudinger-Moser critical equations in \(\mathbb R^2\)
• Critical points of embeddings of \(H_ 0^{1,n}\) into Orlicz spaces
• A priori estimates and existence of positive solutions of semilinear elliptic equations
• Classification of solutions of some nonlinear elliptic equations
• Extremal functions for the Trudinger-Moser inequality in 2 dimensions
• Global compactness properties of semilinear elliptic equations with critical exponential growth
• Critical points of the Moser-Trudinger functional on a disk
• Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two
• Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity
• The Moser-Trudinger inequality and its extremals on a disk via energy estimates
• Multibumps analysis in dimension 2: quantification of blow-up levels
• Blow-up Analysis in Dimension 2 and a Sharp Form of Trudinger–Moser Inequality
• A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface
• Nonexistence of Maxima for Perturbations of Some Inequalities with Critical Growth
• The Lin-Ni’s problem for mean convex domains

This page was built for publication: Non-existence of extremals for the Adimurthi-Druet inequality