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.
core +13 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.
Bonder, J. Fernandez, Silva, A.
core +10 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 fractional Orlicz-Sobolev spaces
, 2023 In this paper, we delve into the well-known concentration-compactness principle in fractional Orlicz-Sobolev spaces, and we apply it to establish the existence of a weak solution for a critical elliptic problem involving the fractional $g ...
Bahrouni, Sabri, Miyagaki, Olimpio
core +4 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 +4 more sources
The concentration-compactness principle for Orlicz spaces and applications
, 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.Comment: 20 pages.
Bonder, Julián Fernández +1 more
core +4 more sources
On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications [PDF]
Fractional Calculus and Applied AnalysisWe obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of ...
Eddine, N. Chems +2 more
core +7 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
Reduction and a Concentration-Compactness Principle for Energy-Casimir Functionals [PDF]
SIAM Journal on Mathematical Analysis, 2001 23 ...
Gerhard Rein
+7 more sources
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
openalex +5 more sources