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

Tommaso Leonori — 2007

Bollettino dell'Unione Matematica Italiana

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 $\sigma$ , $\gamma>0$ .

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Bounded Solutions for Some Dirichlet Problems with L 1 ⁢ ( Ω ) Data

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