Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality

DOI10.1007/S00526-014-0707-ZzbMath1333.46033OpenAlexW1974230134MaRDI QIDQ488127

José Francisco De Oliveira, João Marcos Bezerra do Ó

Publication date: 23 January 2015

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-014-0707-z

zbMATH Keywords

concentration-compactness principleTrudinger-Moser functionalTrudinger-Moser-type inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (3)

Existence for a \(k\)-Hessian equation involving supercritical growth ⋮ Concentration-compactness and extremal problems for a weighted Trudinger–Moser inequality ⋮ On a sharp inequality of Adimurthi-Druet type and extremal functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic equations and systems with critical Trudinger-Moser nonlinearities
• The Liouville-Bratu-Gelfand problem for radial operators
• A sharp form of Moser-Trudinger inequality in high dimension
• Moser-Trudinger inequalities of vector bundle over a compact Riemannian manifold of dimension 2
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Moser-Trudinger type inequalities for the Hessian equation
• Sharp constant and extremal function for the improved Moser-Trudinger inequality involving \(L^p\) norm in two dimension
• Functional analysis, Sobolev spaces and partial differential equations
• Critical points of embeddings of \(H_ 0^{1,n}\) into Orlicz spaces
• Regularity for a more general class of quasilinear equations
• Classification of solutions of some nonlinear elliptic equations
• Extremal functions for the Trudinger-Moser inequality in 2 dimensions
• Observations on Moser's inequality
• Quasilinear elliptic equations with critical exponents
• Positive solutions of critical semilinear elliptic equations on non-contractible planar domains
• Extremals for a Moser-Jodeit exponential inequality.
• Extremals for Moser inequalities
• Semilinear Dirichlet problems for the \(N\)-Laplacian in \(\mathbb{R}^ N\) with nonlinearities in the critical growth range
• Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs
• Cocompactness and minimizers for inequalities of Hardy-Sobolev type involving \(N\)-Laplacian
• Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds
• Blow-up Analysis in Dimension 2 and a Sharp Form of Trudinger–Moser Inequality
• Trudinger-Moser type inequalities for weighted Sobolev spaces involving fractional dimensions
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• ON A CLASS OF QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL EXPONENTS
• Moser's inequality on the ball Bⁿ for functions with mean value zero
• On an inequality by N. Trudinger and J. Moser and related elliptic equations
• Extremal functions for Moser’s inequality

This page was built for publication: Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality