[Existence d'une solution renormalisée des équations quasi linéaires de type Riccati dans les espaces de Lorentz]
Nous prouvons dans cet article l'existence d'une solution renormalisée des équations quasi linéaires de type Riccati avec des données de mesure d'intégrabilité faibles sur les espaces de Lorentz. Le résultat est établi dans les cas réguliers et singuliers. La preuve est basée sur les estimations du gradient pour une solution d'une classe d'équations quasi linéaires elliptiques.
In this paper, we prove the existence of a renormalized solution for the quasilinear Riccati-type equation with low integrability-measure data in Lorentz spaces. The result is established in both regular and singular cases. Our proof is based on the gradient estimates for a solution to a class of quasilinear elliptic equations.
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@article{CRMATH_2019__357_1_59_0,
author = {Tran, Minh-Phuong and Nguyen, Thanh-Nhan},
title = {Existence of a renormalized solution to the quasilinear {Riccati-type} equation in {Lorentz} spaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {59--65},
publisher = {Elsevier},
volume = {357},
number = {1},
year = {2019},
doi = {10.1016/j.crma.2018.12.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.12.001/}
}
TY - JOUR AU - Tran, Minh-Phuong AU - Nguyen, Thanh-Nhan TI - Existence of a renormalized solution to the quasilinear Riccati-type equation in Lorentz spaces JO - Comptes Rendus. Mathématique PY - 2019 SP - 59 EP - 65 VL - 357 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.12.001/ DO - 10.1016/j.crma.2018.12.001 LA - en ID - CRMATH_2019__357_1_59_0 ER -
%0 Journal Article %A Tran, Minh-Phuong %A Nguyen, Thanh-Nhan %T Existence of a renormalized solution to the quasilinear Riccati-type equation in Lorentz spaces %J Comptes Rendus. Mathématique %D 2019 %P 59-65 %V 357 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.12.001/ %R 10.1016/j.crma.2018.12.001 %G en %F CRMATH_2019__357_1_59_0
Tran, Minh-Phuong; Nguyen, Thanh-Nhan. Existence of a renormalized solution to the quasilinear Riccati-type equation in Lorentz spaces. Comptes Rendus. Mathématique, Tome 357 (2019) no. 1, pp. 59-65. doi : 10.1016/j.crma.2018.12.001. http://www.numdam.org/articles/10.1016/j.crma.2018.12.001/
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