Existence of bounded solutions to some nonlinear degenerate elliptic systems
Francesco Leonetti, Pier Vincenzo Petricca · Discrete and Continuous Dynamical Systems - B · 2008
We prove existence of bounded weak solutions$u: \Omega \subset \R^{n} \to \R^{N}$for theDirichlet 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 ellipticoperator and $f$ has enough integrability.