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

Existence of bounded solutions to some nonlinear degenerate elliptic systems

Francesco Leonetti 1, and  Pier Vincenzo Petricca 2,

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.

Keywords: nonlinear, system, bounded, degenerate, solution, Existence, elliptic, coercivit.
Mathematics Subject Classification: Primary: 35J55, 35J60; Secondary: 35J7.
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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