Mathematics in Engineering, 2022 <abstract><p>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. In the first part of the paper, following the main ideas of the pioneering papers of Lions, we prove the CC principle and its variant, that is the
Patrizia Pucci, Letizia Temperini
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Concentration-Compactness Principle for Moser-type Inequalities in Lorentz-Sobolev Spaces [PDF]
Potential Analysis, 2015 Let n ∈ 𝜖, n ≥ 2, q ∈ (1, ∞) and let ${\Omega }\subset \mathbb {R}^{n}$ be an open bounded set. We study the Concentration-Compactness Principle for the embedding of the Lorentz-Sobolev space
Li Dongliang, Zhu Maochun
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Concentration-Compactness Principle for Trudinger–Moser’s Inequalities on Riemannian Manifolds and Heisenberg Groups: A Completely Symmetrization-Free Argument [PDF]
Advanced Nonlinear Studies, 2021 The concentration-compactness principle for the Trudinger–Moser-type inequality in the Euclidean space was established crucially relying on the Pólya–Szegő inequality which allows to adapt the symmetrization argument.
Li Jungang, Lu Guozhen, Zhu Maochun
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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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Solutions of stationary Kirchhoff equations involving nonlocal operators with critical nonlinearity in RN [PDF]
Nonlinear Analysis, 2017 In this paper, we consider the existence and multiplicity of solutions for fractional Schrödinger equations with critical nonlinearity in RN. We use the fractional version of Lions' second concentration-compactness principle and concentration ...
Liang, Sihua +2 more
core +4 more sources
Lower Semicontinuity of Functionals via the Concentration-Compactness Principle
Journal of Mathematical Analysis and Applications, 2001 AbstractIn this paper we show the weak lower semicontinuity of some classes of functionals, using the concentration-compactness principle of P. L. Lions. These functionals involve an integral term, and we do not know whether it can be handled by the De Giorgi theorem.
Eugenio Montefusco
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EXISTENCE OF STEADY STATES FOR THE MAXWELL–SCHRÖDINGER–POISSON SYSTEM: EXPLORING THE APPLICABILITY OF THE CONCENTRATION–COMPACTNESS PRINCIPLE [PDF]
Mathematical Models and Methods in Applied Sciences, 2013 This paper reviews recent results and open problems concerning the existence of steady states to the Maxwell–Schrödinger system. A combination of tools, proofs and results are presented in the framework of the concentration–compactness method.
Catto, Isabelle +3 more
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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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Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities
Open Mathematics, 2012 Abstract Let Ω ⊂ ℝn, n ≥ 2, be a bounded domain and let α < n − 1. Motivated by Theorem I.6 and Remark I.18 of [Lions P.-L., The concentration-compactness principle in the calculus of variations. The limit case. I, Rev. Mat. Iberoamericana, 1985, 1(1), 145–201] and by the results of [Černý R., Cianchi A., Hencl S., Concentration ...
Černý Robert
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Concentration-compactness principle for mountain pass problems
, 2005 In the paper we show that critical sequences associated with the mountain pass level for semilinear elliptic problems on $\R^N$ converge when the non-linearity is subcritical, superlinear and satisfies the penalty condition $F_\infty(s)
Kyril Tintarev
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