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Existence of bounded solutions to some nonlinear degenerate elliptic systems. (English) Zbl 1159.35337
Summary: We prove existence of bounded weak solutions $$u:\Omega\subset\mathbb R^n\to\mathbb R^N$$ for the Dirichlet problem
\begin{aligned} -\operatorname{div} (a(x,u(x),Du(x)))= f(x), &\quad x\in\Omega,\\ u(x)=0, &\quad x \in \partial\Omega\end{aligned}
where $$\Omega$$ is a bounded open set, $$a$$ is a suitable degenerate elliptic operator and $$f$$ has enough integrability.

##### MSC:
 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35J60 Nonlinear elliptic equations 35J70 Degenerate elliptic equations 35D05 Existence of generalized solutions of PDE (MSC2000)
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