Description du défaut de compacité de l'injection de Sobolev

Patrick Gérard

ESAIM: Control, Optimisation and Calculus of Variations (1998)

  • Volume: 3, page 213-233
  • ISSN: 1292-8119

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Gérard, Patrick. "Description du défaut de compacité de l'injection de Sobolev." ESAIM: Control, Optimisation and Calculus of Variations 3 (1998): 213-233. <http://eudml.org/doc/90520>.

@article{Gérard1998,
author = {Gérard, Patrick},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Hilbert homogeneous Sobolev space; almost-orthogonal sum; superposition; sequences of translations and dilations; concentration-compactness principle},
language = {fre},
pages = {213-233},
publisher = {EDP Sciences},
title = {Description du défaut de compacité de l'injection de Sobolev},
url = {http://eudml.org/doc/90520},
volume = {3},
year = {1998},
}

TY - JOUR
AU - Gérard, Patrick
TI - Description du défaut de compacité de l'injection de Sobolev
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1998
PB - EDP Sciences
VL - 3
SP - 213
EP - 233
LA - fre
KW - Hilbert homogeneous Sobolev space; almost-orthogonal sum; superposition; sequences of translations and dilations; concentration-compactness principle
UR - http://eudml.org/doc/90520
ER -

References

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  1. [1] H. Bahouri, P. Gérard : Concentration effects in critical nonlinear wave equations and scattering theory, in Geometrical Optics and Related Topics, F. Colombini and N. Lerner editors, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser, à paraître. Zbl0926.35090MR2033489
  2. [2] H. Bahouri, P. Gérard : High frequency approximation of solutions to critical nonlinear wave equations, prépublication Orsay, 97-34, 1997. 
  3. [3] H. Brezis, J.-M. Coron : Convergence of solutions of H-systems or how to blow bubbles, Arch. Rational Mech. Anal., 89, ( 1985), 21-56. Zbl0584.49024MR784102
  4. [4] J.-Y. Chemin, C.J. Xu : Inclusions de Sobolev en calcul de Weyl-Hörmander et champs de vecteurs sous-elliptiques, Ann. Scient, Éc. Norm. Sup., 30, ( 1997), 719-751. Zbl0892.35161MR1476294
  5. [5] P. Gérard : Oscillations and concentration effects in semilinear dispersive wave equations, J. of Funct. Anal., 141, ( 1996), 60-98. Zbl0868.35075MR1414374
  6. [6] P. Gérard : A microlocal version of concentration-compactness, in Partial Differential Equations and Mathematical Physics, Lars Hörmander and A. Melin editors, Progress in Nonlinear Differential Equations and their Applications, 21, Birkhäuser, 1996. Zbl0868.35005MR1380988
  7. [7] P. Gérard, E. Leichtnam : Ergodic properties of eigenfunctions for the Dirichlet problem, Duke Math. J., 71, ( 1993), 559-607. Zbl0788.35103MR1233448
  8. [8] P. Gérard, P. Markowich, N. Mauser, F. Poupaud : Homogenization limits and Wigner transforms, Comm. Pure and Applied Math. L., ( 1997), 323-379. Zbl0881.35099MR1438151
  9. [9] P. Gérard, Y. Meyer, F. Oru : Inégalités de Sobolev précisées, Séminaire Équations aux Dérivées Partielles 1996-1997, École Polytechnique, et article en préparation. MR1482810
  10. [10] R.A. Hunt : On L(p,q) spaces, L'Enseignement Mathématique, 12, ( 1966), 249-275. Zbl0181.40301MR223874
  11. [11] P.-L. Lions : The concentration-compactness principle in the calculus of variations. The locally compact case, part I, Ann. IHP 1, ( 1984), 109-145. Zbl0541.49009MR778970
  12. [12] P.-L. Lions : The concentration-compactness principle in the calculus of variations. The limit case, part II, Rev. Mat. Iberoamericana 1, ( 1985), 145-201. Zbl0704.49005MR834360
  13. [13] P.-L. Lions, T. Paul : Sur les mesures de Wigner, Revista Mat. Iberoamericana, 9, ( 1993), 553-618. Zbl0801.35117MR1251718
  14. [14] G. Métivier, S. Schochet : Interactions trilinéaires résonantes, Séminaire Équations aux Dérivées Partielles 1995-1996, exposé n° VI, École Polytechnique, Palaiseau. Zbl0885.35066MR1604319
  15. [15] G. Métivier, S. Schochet : Trilinear resonant interactions of semilinear hyperbolic waves, Prépublication 96-31, Institut de Recherche Mathématique de Rennes, Novembre 1996, et Duke Math. J., à paraître. Zbl0955.35007MR1652009
  16. [16] J. Sacks, K. Uhlenbeck : The existence of minimal immersions of 2-spheres, Annals of Math., 113, ( 1981), 1-24. Zbl0462.58014MR604040
  17. [17] M. Struwe : A global compactness result for boundary value problems involving limiting nonlinearities, Math. Z., 187, ( 1984), 511-517. Zbl0535.35025MR760051
  18. [18] H. Wente : Large solutions to the volume constrained Plateau problem, Arch. Rational Mech. Anal., 75, ( 1980), 59-77. Zbl0473.49029MR592104

Citations in EuDML Documents

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  1. Rémi Carles, Clotilde Fermanian–Kammerer, Isabelle Gallagher, Rôle des oscillations quadratiques dans des équations de Schrödinger non linéaire
  2. Isabelle Gallagher, Décomposition en profils pour les solutions des équations de Navier-Stokes
  3. Sahbi Keraani, On the blowup theory for the critical nonlinear Schrödinger equations
  4. Isabelle Gallagher, Profile decomposition for solutions of the Navier-Stokes equations
  5. Gabriel S. Koch, Profile decompositions and applications to Navier-Stokes
  6. Hajer Bahouri, Sur le comportement des solutions d’équations de Schrödinger non linéaires à croissance exponentielle
  7. Carlos E. Kenig, Frank Merle, On the energy critical focusing non-linear wave equation
  8. Jean-Yves Chemin, Isabelle Gallagher, Wellposedness and stability results for the Navier-Stokes equations in 𝐑 3
  9. Hajer Bahouri, Description of the lack of compactness of some critical Sobolev embedding

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