Concentration-compactness principle for embedding into multiple exponential spaces on unbounded domains [PDF]
Czechoslovak Mathematical Journal, 2015 Let Ω ⊂ ℝ n be a domain and let α < n − 1. We prove the Concentration-Compactness Principle for the embedding of the space W 0 1 L n log α
Robert Černý
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Concentration-compactness principle of singular Trudinger–Moser inequality involving N-Finsler–Laplacian operator [PDF]
International Journal of Mathematics, 2020 In this paper, suppose [Formula: see text] be a convex function of class [Formula: see text] which is even and positively homogeneous of degree 1. We establish the Lions type concentration-compactness principle of singular Trudinger–Moser Inequalities involving [Formula: see text]-Finsler–Laplacian operator.
Yanjun Liu
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The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2 [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1984 In this paper (sequel of Part 1) we investigate further applications of the concentration-compactness principle to the solution of various minimization problems in unbounded domains. In particular we present here the solution of minimization problems associated with nonlinear field equations.
Pierre‐Louis Lions
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A study and an application of the concentration compactness type principle
, 2019 In this article we develop a concentration compactness type principle in a variable exponent setup. As an application of this principle we discuss a problem involving fractional `{\it $(p(x),p^+)$-Laplacian}' and power nonlinearities with exponents $(p^+)^*$, $p_s^*(x)$ with the assumption that the critical set $\{x\in :p_s^*(x)=(p^+)^*\}$ is nonempty.
Panda, Akasmika, Choudhuri, Debajyoti
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Concentration-Compactness Principle for embedding into multiple exponential spaces [PDF]
Mathematical Inequalities & Applications, 2012 Let Ω⊂Rn , n 2 , be a bounded domain and let α < n−1 . We prove the ConcentrationCompactness Principle for the embedding of the Orlicz-Sobolev space W 1 0 L n logn−1 L logα logL(Ω) into the Orlicz space corresponding to a Young function that behaves like exp(exp(t n n−1−α )) for large t .
Robert Černɓ
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Journal of Differential Equations, 2002 AbstractFor a bounded domain Ω⊂R2, we establish a concentration-compactness result for the following class of “singular” Liouville equations:−Δu=eu−4π∑j=1mαjδpj in Ω where pj∈Ω, αj>0 and δpj denotes the Dirac measure with pole at point pj, j=1,…,m. Our result extends Brezis–Merle's theorem (Comm.
BARTOLUCCI, DANIELE +1 more
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The concentration-compactness principle for the nonlocal anisotropic
Nonlinear Analysis, 2023 19 ...
Chaker, Jamil +2 more
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Concentration-compactness principle for nonlocal scalar field equations with critical growth
Journal of Mathematical Analysis and Applications, 2017 The aim of this paper is to study a concentration-compactness principle for homogeneous fractional Sobolev space $\mathcal{D}^{s,2} (\mathbb{R}^N)$ for ...
João Marcos do Ó, Diego Ferraz
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Concentration-compactness principle for Trudinger–Moser inequalities on Heisenberg groups and existence of ground state solutions [PDF]
Calculus of Variations and Partial Differential Equations, 2018 Let $\mathbb{H}^{n}=\mathbb{C}^{n}\times\mathbb{R}$ be the $n$-dimensional Heisenberg group, $Q=2n+2$ be the homogeneous dimension of $\mathbb{H}^{n}$. We extend the well-known concentration-compactness principle on finite domains in the Euclidean spaces of \ P. L. Lions to the setting of the Heisenberg group $\mathbb{H}^{n}$.
Guozhen Lu, Maochun Zhu, Jungang Li
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A concentration-compactness principle for perturbed isoperimetric problems with general assumptions
Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article and under mild assumptions we establish existence and density estimates of generalized minimizers of perturbed ...
Jules Candau-Tilh
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