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Article Contents

# Existence of bounded solutions to some nonlinear degenerate elliptic systems

• 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.

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

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