Petits espaces de Lebesgue et quelques applications

Alberto Fiorenza; Jean-Michel Rakotoson

doi:10.1016/S1631-073X(02)02199-4

Petits espaces de Lebesgue et quelques applications
[On small Lebesgue spaces and their applications]

Alberto Fiorenza ¹; Jean-Michel Rakotoson 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

Comptes Rendus. Mathématique, Volume 334 (2002) no. 1, pp. 23-26.

Abstract
Résumé

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.

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.

Received: 2001-07-11
Revised: 2001-11-05
Published online: 2002-01-01

DOI: 10.1016/S1631-073X(02)02199-4

Author's affiliations:

Alberto Fiorenza ¹; Jean-Michel Rakotoson 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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     author = {Alberto Fiorenza and Jean-Michel Rakotoson},
     title = {Petits espaces de {Lebesgue} et quelques applications},
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     pages = {23--26},
     publisher = {Elsevier},
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     number = {1},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02199-4},
     language = {fr},
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Alberto Fiorenza; Jean-Michel Rakotoson. Petits espaces de Lebesgue et quelques applications. Comptes Rendus. Mathématique, Volume 334 (2002) no. 1, pp. 23-26. doi : 10.1016/S1631-073X(02)02199-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02199-4/

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