Concentration-compactness principle for Trudinger-Moser's inequalities on Riemannian manifolds and Heisenberg groups: a completely symmetrization-free argument

DOI10.1515/ans-2021-2147zbMath1486.46039OpenAlexW3205625311WikidataQ115236990 ScholiaQ115236990MaRDI QIDQ2240574

Guozhen Lu, Jun-Gang Li, Maochun Zhu

Publication date: 4 November 2021

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2021-2147

zbMATH Keywords

Heisenberg groupRiemannian manifoldsexponential growthTrudinger-Moser inequalityconcentration-compactness principles

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (17)

A sharpened form of Adams-type inequalities on higher-order Sobolev spaces : a simple approach ⋮ Singular Hardy–Adams inequalities on hyperbolic spaces of any even dimension ⋮ Sharp critical and subcritical trace Trudinger-Moser and Adams inequalities on the upper half-spaces ⋮ Sharp Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on the Siegel domains and complex hyperbolic spaces ⋮ Existence and non-existence of extremals for critical Adams inequality in any even dimension ⋮ Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group ⋮ Gagliardo-Nirenberg type inequalities on Lorentz, Marcinkiewicz and weak-𝐿^{∞} spaces ⋮ Existence of extremals for Trudinger-Moser inequalities involved with a trapping potential ⋮ Least energy solutions to quasilinear subelliptic equations with constant and degenerate potentials on the Heisenberg group ⋮ Critical and supercritical Adams' inequalities with logarithmic weights ⋮ Existence and non-existence of ground states of bi-harmonic equations involving constant and degenerate Rabinowitz potentials ⋮ An improved Trudinger-Moser inequality involving \(N\)-Finsler-Laplacian and \(L^p\) norm ⋮ Equivalence of subcritical and critical Adams inequalities in \(W^{m,2}(\mathbb{R}^{2m})\) and existence and non-existence of extremals for Adams inequalities under inhomogeneous constraints ⋮ Existence of sign-changing radial solutions with prescribed numbers of zeros for elliptic equations with the critical exponential growth in ℝ² ⋮ Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals ⋮ Concentration-compactness principle associated with Adams' inequality in Lorentz-Sobolev space ⋮ Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp affine and improved Moser-Trudinger-Adams type inequalities on unbounded domains in the spirit of Lions
• The concentration-compactness principle in the calculus of variations. The limit case. I
• On a quasilinear nonhomogeneous elliptic equation with critical growth in \(\mathbb R^N\)
• A sharp inequality of J. Moser for higher order derivatives
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• Concentration-compactness principle for Trudinger-Moser inequalities on Heisenberg groups and existence of ground state solutions
• Sharpened Adams inequality and ground state solutions to the bi-Laplacian equation in \(\mathbb{R}^4\)
• Concentration-compactness principle of singular Trudinger-Moser inequalities in \(\mathbb{R}^n\) and \(n\)-Laplace equations
• Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities
• Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications
• \(N\)-Laplacian equations in \(\mathbb{R}^N\) with critical growth
• Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs
• Hardy-Adams inequalities on \(\mathbb{H}^2 \times \mathbb{R}^{n-2} \)
• Critical and subcritical Trudinger-Moser inequalities on complete noncompact Riemannian manifolds
• Rearrangements in Carnot groups
• Sharp singular Trudinger-Moser inequalities under different norms
• Existence and nonexistence of extremal functions for sharp Trudinger-Moser inequalities
• Concentration-compactness principle for the sharp Adams inequalities in bounded domains and whole space \(\mathbb{R}^n\)
• Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds
• Trudinger-Moser inequalities in fractional Sobolev-Slobodeckij spaces and multiplicity of weak solutions to the fractional-Laplacian equation
• A new approach to sharp Moser-Trudinger and Adams type inequalities: a rearrangement-free argument
• Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs
• Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
• Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R
• Best constants for Moser-Trudinger inequalities on the Heisenberg group
• On Nonuniformly Subelliptic Equations of Q−sub-Laplacian Type with Critical Growth in the Heisenberg Group
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
• Improved <scp>Moser‐Trudinger‐Onofri</scp> Inequality under Constraints
• A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb{R}^n$
• A Remark on the Concentration Compactness Principle in Critical Dimension

This page was built for publication: Concentration-compactness principle for Trudinger-Moser's inequalities on Riemannian manifolds and Heisenberg groups: a completely symmetrization-free argument