Remarques sur l'analyse semi-classique de l'équation de Schrödinger non linéaire
Compacité par compensation et régularité 2-microlocale
Mesures semi-classiques et ondes de Bloch
Moyennes de solutions d'équations aux dérivées partielles
Sur l'équation des ondes non linéaires avec exposant critique
Injections de Sobolev critiques, mesures microlocales et ondes non linéaires
The Cauchy problem for the Gross–Pitaevskii equation
Description of the lack of compactness for the Sobolev imbedding
We prove that any bounded sequence in a Hilbert homogeneous Sobolev space has a subsequence which can be decomposed as an almost-orthogonal sum of a sequence going strongly to zero in the corresponding Lebesgue space, and of a superposition of terms obtained from fixed profiles by applying sequences of translations and dilations. This decomposition contains in particular the various versions of the concentration-compactness principle.
On nonlinear Schrödinger equations in exterior domains
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