Existence of bounded solutions to some nonlinear degenerate elliptic systems

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

Received: November 2007

Revised: June 2008

Published: July 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J55, 35J60; Secondary: 35J7.

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