A Microlocal Version of Concentration-Compactness

  • Patrick Gérard
Conference paper
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 21)


The concentration-compactness principle has been developed by P.-L. Lions [10] in order to study minimizing sequences of elliptic variational problems displaying some lack of compactness. It is closely related to the general problem of describing the sequences of functions on Rd which violate locally the compactness of the Sobolev imbedding
$$ {H^S}{\mkern 1mu} \left( {{\mathbb{R}^d}} \right){\mkern 1mu} \to {\mkern 1mu} {L^P}{\mkern 1mu} \left( {{\mathbb{R}^d}} \right),{\mkern 1mu} 0 < {\mkern 1mu} s < {\mkern 1mu} \frac{d}{2},{\mkern 1mu} \frac{1}{p}{\mkern 1mu} = {\mkern 1mu} \frac{1}{2}{\mkern 1mu} - {\mkern 1mu} \frac{s}{d}. $$


Nonlinear Wave Equation Linear Wave Equation Satisfying Assumption Semiclassical Measure Finite Propagation Speed 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Patrick Gérard
    • 1
  1. 1.Département de MathématiquesUniversité de Paris-SudOrsay CedexFrance

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