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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@article{CRMATH_2002__334_1_23_0,
author = {Fiorenza, Alberto and Rakotoson, Jean-Michel},
title = {Petits espaces de {Lebesgue} et quelques applications},
journal = {Comptes Rendus. Math\'ematique},
pages = {23--26},
publisher = {Elsevier},
volume = {334},
number = {1},
year = {2002},
doi = {10.1016/S1631-073X(02)02199-4},
language = {fr},
url = {https://www.numdam.org/articles/10.1016/S1631-073X(02)02199-4/}
}
TY - JOUR AU - Fiorenza, Alberto AU - Rakotoson, Jean-Michel TI - Petits espaces de Lebesgue et quelques applications JO - Comptes Rendus. Mathématique PY - 2002 SP - 23 EP - 26 VL - 334 IS - 1 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/S1631-073X(02)02199-4/ DO - 10.1016/S1631-073X(02)02199-4 LA - fr ID - CRMATH_2002__334_1_23_0 ER -
%0 Journal Article %A Fiorenza, Alberto %A Rakotoson, Jean-Michel %T Petits espaces de Lebesgue et quelques applications %J Comptes Rendus. Mathématique %D 2002 %P 23-26 %V 334 %N 1 %I Elsevier %U https://www.numdam.org/articles/10.1016/S1631-073X(02)02199-4/ %R 10.1016/S1631-073X(02)02199-4 %G fr %F CRMATH_2002__334_1_23_0
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. https://www.numdam.org/articles/10.1016/S1631-073X(02)02199-4/
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