A note on quasilinear elliptic systems with $L^\infty$-data

We prove the existence of a weak energy solution for the boundary value problem
\begin{eqnarray*} -\mathrm{div}\, a(x, u, Du) &=& f \text{ in } \Omega,\\ u &=& 0 \text{ on } \partial\Omega, \end{eqnarray*}
where $\Omega$ is a smooth bounded open domain in $\mathbb{R}^n$ ($n\geqslant 3$) and $f\in L^\infty(\Omega;\mathbb{R}^m)$. The existence result is proved using the concept of Young measures.