A-priori gradient bound for elliptic systems under either slow or fast growth conditions

Tommaso Di Marco, Paolo Marcellini

We obtain an a-priori $W_{loc}^{1,\infty }(\Omega ;{\mathbb{R}}^m)-$bound for solutions in $\Omega \subset {\mathbb{R}}^n$, $n\ge 2$, to the elliptic system \begin{equation*} \sum_{i=1…