Characterization of the lack of compactness of $H^2_{\rm rad}({\mathbb R}^4)$ into the Orlicz space

DOI10.1142/S0219199713500375zbMath1310.46033arXiv1301.4475OpenAlexW2087580671MaRDI QIDQ2876617

Mohamed Khalil Zghal, Ines Ben Ayed

Publication date: 19 August 2014

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4475

zbMATH Keywords

Sobolev spaceOrlicz spacelack of compactnessAdams' inequalitySobolev critical exonent

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33)

Related Items (4)

Logarithmic Littlewood-Paley Decomposition and Applications to Orlicz Spaces ⋮ On the behavior of solutions of nonlinear Schrödinger equation with exponential growth ⋮ Sharp Adams-type inequality invoking Hardy inequalities ⋮ Structure theorems for 2D linear and nonlinear Schrödinger equations

Cites Work

• 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
• On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold
• A general wavelet-based profile decomposition in the critical embedding of function spaces
• 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
• Convergence of solutions of H-systems or how to blow bubbles
• Analysis of the lack of compactness in the critical Sobolev embeddings
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• Fourier Analysis and Nonlinear Partial Differential Equations
• Description of the lack of compactness for the Sobolev imbedding
• High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations
• Sharp Adams-type inequalities in ℝⁿ
• Lack of compactness in the 2D critical Sobolev embedding, the general case
• On the defect of compactness for the Strichartz estimates of the Schrödinger equations

This page was built for publication: Characterization of the lack of compactness of $H^2_{\rm rad}({\mathbb R}^4)$ into the Orlicz space