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The Concentration-Compactness Principle for Fractional Orlicz-Sobolev Spaces

Complex Variables and Elliptic Equations
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 $g-$Laplacian.
Bahrouni, Sabri, Miyagaki, Olimpio
exaly   +3 more sources

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The principle of concentration compactness in spaces and its application

Nonlinear Analysis: Theory, Methods & Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Concentration-Compactness principle for Trudinger–Moser inequalities with logarithmic weights and their applications

Nonlinear Analysis, 2020
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Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality

Calculus of Variations and Partial Differential Equations, 2014
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De Oliveira, José Francisco, Do Ó, João Marcos   +1 more
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The Compact Embeddings and the Concentration-Compactness Principles for Anisotropic Variable Exponent Sobolev Spaces and Applications

Journal of Geometric Analysis
Abstract In this paper, we present new results about the compact embeddings of anisotropic variable exponent Sobolev spaces into variable Lebesgue spaces. We also refine and extend the concentration–compactness principle to trace embeddings in these spaces.
Maria Alessandra Ragusa, Nabil Chems Eddine   +1 more
exaly   +2 more sources

Concentration–Compactness Principle to a Weighted Moser–Trudinger Inequality and Its Application

Journal of Mathematics
We employ level‐set analysis of functions to establish a sharp concentration–compactness principle for the Moser–Trudinger inequality with power weights in . Furthermore, we systematically prove the existence of ground state solutions to the associated nonlinear partial differential equation.
exaly   +2 more sources

The concentration‐compactness principle and the asymptotic behavior for some degenerate parabolic equation

Asymptotic Analysis, 2003
In this paper we study the existence and asymptotic behavior of the global solutions of some degenerate parabolic equation with critical Sobolev exponent. In particular, we apply the concentration‐compactness principle of P.‐L. Lions to the study of the asymptotic behavior of global solutions with the initial value in “stable set”.
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The concentration-compactness principle in the calculus of variations. The locally compact case. I

1984
This paper presents a general method - called concentration-compactness method - for solving certain minimization problems on unbounded domains. This method applies to problems with some form of local compactness. For minimization problems with constraints, sub-additivity inequalities are obtained for the infimum of the problem considered as a function
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The Concentration-Compactness Principles for Ws,p(·,·)(ℝN) and Application

Advances in Nonlinear Analysis, 2021
Ky Ho, Yun-Ho Kim
exaly  

Concentration-Compactness Principle Associated With Adams' Inequality in Lorentz-Sobolev Space

Advanced Nonlinear Studies, 2022
Maochun Zhu
exaly