Concentration compactness principles for the systems of critical elliptic equations [PDF]
Differential Equations & Applications, 2012 In this paper, some important variants of the concentration compactness principle are established. By the variants, some kinds of the elliptic systems can be investigated and the existence of nontrivial solutions to the systems can be verified by the variational methods.
Dongsheng Kang
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The concentration-compactness principles for W s,p (·,·) (ℝ N ) and application [PDF]
Advances in Nonlinear Analysis, 2020 Abstract We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.
Ky Ho, Yun-Ho Kim
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Concentration-compactness principles for Moser–Trudinger inequalities: new results and proofs [PDF]
Annali di Matematica Pura ed Applicata, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Robert Černý +2 more
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The concentration-compactness principles for $W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)$ and application [PDF]
, 2019 We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.
Ky Ho, Yun-Ho Kim
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The Compact Embeddings and the Concentration-Compactness Principles for Anisotropic Variable Exponent Sobolev Spaces and Applications [PDF]
The Journal of Geometric AnalysisAbstract 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.
Nabil Chems Eddine +1 more
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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.
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An abstract version of the concentration compactness principle
Revista Matemática Complutense, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Schindler, I., Tintarev, K.
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Semiclassical stationary states for nonlinear Schr\"odinger equations under a strong external magnetic field [PDF]
, 2015 We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega, \end{aligned}
Di Cosmo, Jonathan +1 more
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Connecting the realms of urban form, density and microclimate [PDF]
, 2018 Av doktorgradsstudenter på norske universiteter, er det en fjerdedel som ikke fullfører innen normert tid. Det er lite forskning på hvorfor det er slik i Norge.
Emmanuel, Rohinton, Steemers, Koen
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Some Progress in Conformal Geometry [PDF]
, 2007 This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion.
Chang, Sun-Yung A. +2 more
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