Vanishing-concentration-compactness alternative for critical Sobolev embedding with a general integrand in \(\mathbb{R}^2\)

DOI10.1007/s00526-021-02076-5zbMath1494.47124OpenAlexW3195398752WikidataQ115386435 ScholiaQ115386435MaRDI QIDQ2050167

Michinori Ishiwata, Hidemitsu Wadade

Publication date: 30 August 2021

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

Full work available at URL: https://doi.org/10.1007/s00526-021-02076-5

zbMATH Keywords

maximizing problemMoser-Pohozaev-Trudinger-Yudovich type inequalityvanishing-concentration-compactness alternative

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10)

Cites Work

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• On the effect of equivalent constraints on a maximizing problem associated with the Sobolev type embeddings in \(\mathbb R^N\)
• Sharp singular Adams inequalities in high order Sobolev spaces
• Equivalent Moser type inequalities in \(\mathbb{R}^2\) and the zero mass case
• Existence and nonexistence of maximizers for variational problems associated with Trudinger--Moser type inequalities in \({\mathbb{R}^N}\)
• Extremal functions for singular Trudinger-Moser inequalities in the entire Euclidean space
• On the sharp constant for the weighted Trudinger-Moser type inequality of the scaling invariant form
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Trudinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger mixed problem
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Critical points of embeddings of \(H_ 0^{1,n}\) into Orlicz spaces
• Extremal functions for the Trudinger-Moser inequality in 2 dimensions
• Existence of solitary waves in higher dimensions
• Characterization of Trudinger's inequality
• Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities
• Existence and non-existence of maximizers for the Moser-Trudinger type inequalities under inhomogeneous constraints
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• \(N\)-Laplacian equations in \(\mathbb{R}^N\) with critical growth
• On critical cases of Sobolev's inequalities
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations
• Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R
• Vanishing-concentration-compactness alternative for the Trudinger–Moser inequality in ℝN
• Extremal functions for Moser’s inequality
• Maximizers for the singular Trudinger-Moser inequalities in the subcritical cases
• A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb{R}^n$