The concentration-compactness principle in the Calculus of Variations

@inproceedings{Lions1984TheCP,
  title={The concentration-compactness principle in the Calculus of Variations},
  author={Pierre-Louis Lions},
  year={1984}
}
  • P. Lions
  • Published 1 March 1984
  • Mathematics
Compactness and quasilinear problems with critical exponents
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Lower Semicontinuity of Functionals via the Concentration-Compactness Principle
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. - We prove here the existence of a positive solution, under general conditions, for semilinear elliptic equations in unbounded domains with a variational structure. The solutions we build cannot be
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We prove some refinements of concentration compactness principle for Sobolev space $W^{1,n}$ on a smooth compact Riemannian manifold of dimension $n$. As an application, we extend Aubin's theorem for
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The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem
In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the
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