A sharp inequality of Trudinger-Moser type and extremal functions in \(H^{1, n}(\mathbb{R}^n)\)

DOI10.1016/j.jde.2015.01.026zbMath1327.35459OpenAlexW2065862471MaRDI QIDQ2339465

João Marcos Bezerra do Ó, Manassés de Souza

Publication date: 1 April 2015

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

Full work available at URL: https://doi.org/10.1016/j.jde.2015.01.026

zbMATH Keywords

sharp constantsTrudinger-Moser inequalityextremal functionblow-up analysislimiting Sobolev inequalities

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) Partial differential inequalities and systems of partial differential inequalities (35R45) Nonlinear elliptic equations (35J60)

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Cites Work

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• Elliptic equations and systems with critical Trudinger-Moser nonlinearities
• A quasi-linear elliptic equation with critical growth on compact Riemannian manifold without boundary
• Nonlinear scalar field equations. I: Existence of a ground state
• A sharp form of Moser-Trudinger inequality in high dimension
• The concentration-compactness principle in the calculus of variations. The limit case. I
• A nonhomogeneous elliptic problem involving critical growth in dimension two
• Sharp constant and extremal function for the improved Moser-Trudinger inequality involving \(L^p\) norm in two dimension
• Singular solutions of the \(p\)-Laplace equation
• Critical points of embeddings of \(H_ 0^{1,n}\) into Orlicz spaces
• Regularity for a more general class of quasilinear equations
• Extremal functions for the Trudinger-Moser inequality in 2 dimensions
• Existence of solitary waves in higher dimensions
• Global compactness properties of semilinear elliptic equations with critical exponential growth
• Positive solutions of critical semilinear elliptic equations on non-contractible planar domains
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• \(N\)-Laplacian equations in \(\mathbb{R}^N\) with critical growth
• Semilinear Dirichlet problems for the \(N\)-Laplacian in \(\mathbb{R}^ N\) with nonlinearities in the critical growth range
• Nontrivial solution of a quasilinear elliptic equation with critical growth in \(\mathbb{R}^ n\)
• Local behavior of solutions of quasi-linear equations
• An improvement for the Trudinger-Moser inequality and applications
• Espaces d'interpolation et théorème de Soboleff
• 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
• A sharp Trudinger-Moser type inequality in $\mathbb {R}^2$
• Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R
• On an inequality by N. Trudinger and J. Moser and related elliptic equations
• Extremal functions for Moser’s inequality
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
• A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb{R}^n$

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