Lack of compactness in the 2D critical Sobolev embedding, the general case

DOI10.1016/j.crma.2012.01.016zbMath1246.46028arXiv1112.2998OpenAlexW2962855219MaRDI QIDQ5895549

Hajer Bahouri, Nader Masmoudi, Mohamed Majdoub

Publication date: 22 March 2012

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série, Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.2998

zbMATH Keywords

capacitycompactnessOrlicz spaceSobolev critical exponentTrudinger-Moser inequalitySobolev embeddingSchwarz symmetrizationlack of compactness

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items

Logarithmic Littlewood-Paley Decomposition and Applications to Orlicz Spaces, About the behavior of regular Navier-Stokes solutions near the blow up, On the stability of global solutions to the three-dimensional Navier-Stokes equations, On the behavior of solutions of nonlinear Schrödinger equation with exponential growth, The Littlewood-Paley theory: a common thread of many works in nonlinear analysis, On the defect of compactness in Sobolev embeddings on Riemannian manifolds, High frequency approximation of solutions to Klein–Gordon equation in Orlicz framework, Concentration profiles for the Trudinger-Moser functional are shaped like toy pyramids, Sharp Adams-type inequality invoking Hardy inequalities, Structure theorems for 2D linear and nonlinear Schrödinger equations, Adams' Inequality with the Exact Growth Condition in ℝ⁴, Characterization of the lack of compactness of $H^2_{\rm rad}({\mathbb R}^4)$ into the Orlicz space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the stability in weak topology of the set of global solutions to the Navier-Stokes equations
• On the lack of compactness in the 2D critical Sobolev embedding
• Global well-posedness of the Cauchy problem for a super-critical nonlinear wave equation in two space dimensions
• Qualitative study of the critical wave equation with a subcritical perturbation
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Remarks on Gagliardo-Nirenberg type inequality with critical Sobolev space and BMO
• Convergence of solutions of H-systems or how to blow bubbles
• Critical points of embeddings of \(H_ 0^{1,n}\) into Orlicz spaces
• A sharp inequality of J. Moser for higher order derivatives
• Extremal functions for the Trudinger-Moser inequality in 2 dimensions
• Analysis of the lack of compactness in the critical Sobolev embeddings
• Comparison of linear and nonlinear waves with variable coefficients
• Global compactness properties of semilinear elliptic equations with critical exponential growth
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space
• Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
• Scattering for the critical 2-D NLS with exponential growth.
• Variation and optimization of formes. A geometric analysis
• Multibumps analysis in dimension 2: quantification of blow-up levels
• Description of the compactness defect of the Sobolev embedding into the Heisenberg group
• An elementary proof of sharp Sobolev embeddings
• Fourier Analysis and Nonlinear Partial Differential Equations
• Blow-up Analysis in Dimension 2 and a Sharp Form of Trudinger–Moser Inequality
• Double logarithmic inequality with a sharp constant
• Imbedding theorems of Sobolev type in potential theory.
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Description of the lack of compactness for the Sobolev imbedding
• High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations
• A sharp embedding theorem for Orlicz-Sobolev spaces
• Sobolev imbedding theorems in borderline cases
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
• On compactness in the Trüdinger-Moser inequality
• On the Elements Involved in the Lack of Compactness in Critical Sobolev Embedding
• On the sharpness of a limiting case of the Sobolev imbedding theorem
• An abstract version of the concentration compactness principle.
• On the defect of compactness for the Strichartz estimates of the Schrödinger equations