A study and an application of the concentration compactness type principle [PDF]
, 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.
Akasmika Panda, Debajyoti Choudhuri
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Concentration-Compactness Principle for Generalized Trudinger Inequalities
Zeitschrift für Analysis und ihre Anwendungen, 2011 Let \Omega\subset\mathbb R^n , n\geq 2 , be a bounded domain and let \alpha < n-1
Robert Černý +2 more
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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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Concentration-compactness principle of singular Trudinger-Moser inequality involving $N$-Finsler-Laplacian operator [PDF]
International Journal of Mathematics, 2019 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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Reduction and a concentration-compactness principle for energy-Casimir functionals [PDF]
SIAM Journal on Mathematical Analysis, 2001 23 ...
Gerhard Rein
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A Remark on the Concentration Compactness Principle in Critical Dimension [PDF]
Communications on Pure and Applied Mathematics, 2021 AbstractWe prove some refinements of the concentration compactness principle for Sobolev space W1, n on a smooth compact Riemannian manifold of dimension n. As an application, we extend Aubin's theorem for functions on with zero first‐order moments of the area element to the higher‐order moments case.
Fengbo Hang
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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, 2017 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 $\mathbb{H}^{n}$.
Jungang Li, Guozhen Lu, Maochun Zhu
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The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order [PDF]
Nonlinear Analysis, 2021 19 ...
Jamil Chaker +2 more
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Advanced Nonlinear Studies, 2018 In this paper, we use the rearrangement-free argument, in the spirit of the work by Li, Lu and Zhu [25], on the concentration-compactness principle on the Heisenberg group to establish a sharpened version of the singular Lions concentration-compactness ...
Zhang Caifeng, Chen Lu
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Lower Semicontinuity of Functionals via the Concentration-Compactness Principle
Journal of Mathematical Analysis and Applications, 2001 It is proved that, if \(\Omega\) is a bounded open subset of \({\mathbb R}^N\) and ...
Eugenio Montefusco
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