Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data

Leonori, Tommaso

Bounded Solutions for Some Dirichlet Problems with

L^{1}(\Omega)

Data

Leonori, Tommaso

Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 785-795 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

In this paper we prove the existence of a solution for a problem whose model is: $\begin{cases}-\Delta u+\frac{u}{\sigma-|u|}=\gamma|\nabla u|^{2}+f(x)&\text{in% }\Omega\\ u=0&\text{on }\partial\Omega\end{cases}$ with $f(x)$ in $L^{1}(\Omega)$ and $\sigma$ , $\gamma>0$ .

In questo lavoro viene dimostrata l'esistenza di una soluzione per un problema il cui modello è: $\begin{cases}-\Delta u+\frac{u}{\sigma-|u|}=\gamma|\nabla u|^{2}+f(x)&\text{in% }\Omega\\ u=0&\text{on }\partial\Omega\end{cases}$ con $f(x)$ in $L^{1}(\Omega)$ e $\sigma$ , $\gamma>0$ .

Publié le : 2007-10-01

MR 2507896 | Zbl 1184.35129

@article{BUMI_2007_8_10B_3_785_0,
     author = {Tommaso Leonori},
     title = {Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {785-795},
     zbl = {1184.35129},
     mrnumber = {2507896},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_785_0}
}

Leonori, Tommaso. Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 785-795. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_785_0/

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