# American Institute of Mathematical Sciences

2009, 11(1): 191-203. doi: 10.3934/dcdsb.2009.11.191

## Existence of bounded solutions to some nonlinear degenerate elliptic systems

 1 Università di L'Aquila, Dipartimento di Matematica Pura ed Applicata, Via Vetoio, Coppito, 67100 L'Aquila, Italy 2 Via Sant’Amasio 18, 03039 Sora, Italy

Received  November 2007 Revised  June 2008 Published  November 2008

We prove existence of bounded weak solutions $u: \Omega \subset \R^{n} \to \R^{N}$ for the Dirichlet problem

-div $( a(x, u(x), Du(x) ) ) = f(x),$ $x \in \Omega$;
$u(x) = 0,$ $x \in \partial\Omega$

where $\Omega$ is a bounded open set, $a$ is a suitable degenerate elliptic operator and $f$ has enough integrability.

Citation: Francesco Leonetti, Pier Vincenzo Petricca. Existence of bounded solutions to some nonlinear degenerate elliptic systems. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 191-203. doi: 10.3934/dcdsb.2009.11.191
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