Petits espaces de Lebesgue et quelques applications
Fiorenza, Alberto1 ; Rakotoson, Jean-Michel2
1 Dipartimento di Costruzioni e Metodi Matematici in Architettura, Universitá di Napoli “Federico II”, via Monteoliveto, 3, I-80134 Napoli, Italy
2 Laboratoire d'applications des mathématiques, Téléport 2 Département de mathématiques, Université de Poitiers, BP 30179, 86962 Futuroscope Chasseneuil cedex, France
Comptes Rendus. Mathématique, Tome 334 (2002) no. 1, pp. 23-26.

On se propose d'établir quelques propriétés des petits espaces de Lebesgue introduits par Fiorenza [7], notamment la convergence monotone de Lévi et des propriétés d'équivalence de normes. En combinant ces propriétés avec les inégalités de Poincaré–Sobolev pour le réarrangement relatif [11], nous donnons quelques estimations précises concernant les espaces de Sobolev associés à ces espaces et les régularités des solutions d'équations quasilinéaires lorsque les données sont dans ces espaces.

We prove some new properties of the small Lebesgue spaces introduced by Fiorenza [7]. Combining these properties with the Poincaré–Sobolev inequalities for the relative rearrangement (see [11]), we derive some new and precises estimates either for small Lebesgue–Sobolev spaces or for quasilinear equations with data in the small Lebesgue spaces.

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DOI : 10.1016/S1631-073X(02)02199-4
Fiorenza, Alberto 1 ; Rakotoson, Jean-Michel 2

1 Dipartimento di Costruzioni e Metodi Matematici in Architettura, Universitá di Napoli “Federico II”, via Monteoliveto, 3, I-80134 Napoli, Italy
2 Laboratoire d'applications des mathématiques, Téléport 2 Département de mathématiques, Université de Poitiers, BP 30179, 86962 Futuroscope Chasseneuil cedex, France 
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Fiorenza, Alberto; Rakotoson, Jean-Michel. Petits espaces de Lebesgue et quelques applications. Comptes Rendus. Mathématique, Tome 334 (2002) no. 1, pp. 23-26. doi : 10.1016/S1631-073X(02)02199-4. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02199-4/

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