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Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality

Calculus of Variations and Partial Differential Equations, 2014
We prove a concentration-compactness principle for the Trudinger-Moser functional associated with a class of weighted Sobolev spaces including fractional dimensions. Based in this result and using blow up analysis we establish a sharp form of Trudinger-Moser type inequality for this class of weighted Sobolev spaces.
José Francisco de Oliveira   +2 more
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The principle of concentration compactness in spaces and its application

Nonlinear Analysis: Theory, Methods & Applications, 2009
Abstract In this paper we establish a principle of concentration compactness in L p ( x ) spaces and apply it to obtain the existence of solutions for p ( x ) -Laplacian equations with critical growth.
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Concentration-Compactness principle for Trudinger–Moser inequalities with logarithmic weights and their applications

Nonlinear Analysis, 2020
Abstract In this paper, we establish a sharp concentration-compactness principle associated with the Trudinger–Moser inequality on Sobolev spaces with logarithmic weights. As applications, we establish the existence of ground state solutions to the following equation with critical double exponential nonlinearity − d i v ( | ∇ u |
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Concentration-compactness principle at infinity and semilinear elliptic equations involving critical and subcritical Sobolev exponents

Calculus of Variations and Partial Differential Equations, 1995
We formulate the concentration-compactness principle at infinity for both subcritical and critical case. We show some applications to the existence theory of semilinear elliptic equations involving critical and subcritical Sobolev exponents.
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Concentration compactness principle at infinity with partial symmetry and its application

Nonlinear Analysis: Theory, Methods & Applications, 2002
Michinori Ishiwata, Mitsuharu Ôtani
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Concentration compactness principle and quasilinear elliptic equations in Rn

Communications in Partial Differential Equations, 1991
Marion Badiale, Citti Giovanna
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