Geodesic
Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 785-795.

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In this paper we prove the existence of a solution for a problem whose model is: \begin{equation*} \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} \end{equation*} 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{equation*} \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} \end{equation*} con $f(x)$ in $L^{1}(\Omega)$ e $\sigma$, $\gamma > 0$. 
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     title = {Bounded {Solutions} for {Some} {Dirichlet} {Problems} with $L^1(\Omega)$ {Data}},
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Leonori, Tommaso. Bounded Solutions for Some Dirichlet Problems with $L^1(\Omega)$ Data. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 785-795. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a22/

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