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| HAL : hal-00344212, version 1 |
| arXiv : 0812.0927 |
| Fiche détaillée |  Récupérer au format |
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| Differential and integral equations 20, 1 (2006) 77-92 |
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| On local compactness in quasilinear elliptic problems |
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| Khalid Adriouch 1Abdallah El Hamidi 2 |
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| (01/08/2006) |
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| One of the major difficulties in nonlinear elliptic problems involving critical nonlinearities is the compactness of Palais-Smale sequences. In their celebrated work \cite{BN}, Brézis and Nirenberg introduced the notion of critical level for these sequences in the case of a critical perturbation of the Laplacian homogeneous eigenvalue problem. In this paper, we give a natural and general formula of the critical level for a large class of nonlinear elliptic critical problems. The sharpness of our formula is established by the construction of suitable Palais-Smale sequences which are not relatively compact. |
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| 1 : | Laboratoire de Mathématiques et Applications (LMA-Rochelle) |
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Université de La Rochelle |
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| 2 : | Mathématiques, Image et Applications (MIA) |
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Université de La Rochelle : EA3165 |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| local compactness – critical exponent – best sobolev constant |
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| hal-00344212, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00344212 | |
| oai:hal.archives-ouvertes.fr:hal-00344212 | |
| Contributeur : Abdallah El Hamidi | |
| Soumis le : Jeudi 4 Décembre 2008, 10:51:42 | |
| Dernière modification le : Jeudi 4 Décembre 2008, 13:44:52 | |
