for a.e. $x\in U$ and every $\xi\in\mathbb R^n$. Then $u$ has a locally Hölder continuous representative: whenever $V\subset\subset W\subset\subset U$, there are $\alpha\in(0,1)$ and $C>0$, depending on $n$, $\theta$, $\|a\|_{L^\infty(W)}$, $V$, and $W$, such that