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 ...
Ian Schindler, Cyril Tintarev
core +9 more sources
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.
Li Dongliang, Zhu Maochun
doaj +5 more sources
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.
Julián Fernández Bonder, Analía Silva
core +12 more sources
Mathematics in Engineering, 2023 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
doaj +5 more sources
Concentration–Compactness Principle to a Weighted Moser–Trudinger Inequality and Its Application
Journal of MathematicsWe employ level-set analysis of functions to establish a sharp concentration–compactness principle for the Moser–Trudinger inequality with power weights in R+2.
Yubo Ni
doaj +3 more sources
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
doaj +2 more sources
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
doaj +3 more sources
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
doaj +2 more sources
A remark on the concentration compactness principle in critical dimension [PDF]
Communications on Pure and Applied Mathematics, 2020 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
openalex +4 more sources
Concentration-compactness principle for mountain pass problems [PDF]
, 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
openalex +3 more sources