An abstract version of the concentration compactness principle [PDF]
Revista Matemática Complutense, 2002 We prove an abstract version of concentration compactness principle in Hilbert space and show its applications to a range of elliptic problems on unbounded domains.We prove an abstract version of concentration compactness principle in Hilbert space and ...
Schindler, I., Tintarev, K.
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A Remark on the Concentration Compactness Principle in Critical Dimension [PDF]
Communications on Pure and Applied Mathematics, 2021 We 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 Sn with zero first‐order moments of the ...
Fengbo Hang
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The concentration–compactness principle for Orlicz spaces and applications [PDF]
Mathematische Nachrichten, 2021 In this paper, we extend the well‐known concentration–compactness principle of P.L. Lions to Orlicz spaces. As an application, we show an existence result to some critical elliptic problem with nonstandard growth.
Julián Fernández Bonder, Analía Silva
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Reduction and a Concentration-Compactness Principle for Energy-Casimir Functionals [PDF]
SIAM Journal on Mathematical Analysis, 2001 Energy-Casimir functionals are a useful tool for the construction of steady states and the analysis of their nonlinear stability properties for a variety of conservative systems in mathematical physics. Recently, Y.
Gerhard Rein
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The concentration-compactness principle for variable exponent spaces and applications [PDF]
Electronic Journal of Differential Equations, 2009 In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to the variable exponent case.
Bonder, J. Fernandez, Silva, A.
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Mathematics in Engineering, 2022 In this paper we establish some variants of the celebrated concentration–compactness principle of Lions – CC principle briefly – in the classical and fractional Folland–Stein spaces.
Patrizia Pucci, Letizia Temperini
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Concentration-compactness principle associated with Adams' inequality in Lorentz-Sobolev space [PDF]
Advanced Nonlinear Studies, 2022 The concentration-compactness principle of Lions type in Euclidean space relies on the Pólya-Szegö inequality, which is not available in non-Euclidean settings.
Dongliang Li, Maochun Zhu
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The Concentration-Compactness Principle in the Calculus of Variations. The limit case, Part 1
Revista Matemática Iberoamericana, 1985 After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in \mathbb R^N where the invariance of \mathbb R^N
Pierre‐Louis Lions
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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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The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. [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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