  We construct a function $u \in W^{1,1}_{\mathrm{loc}} (B(0,1))$ which is a
solution to $\Div (A \nabla u)=0$ in the sense of distributions, where $A$ is
continuous and $u \not \in W^{1,p}_{\mathrm{loc}} (B(0,1))$ for $p > 1$. We
also give a function $u \in W^{1,1}_{\mathrm{loc}} (B(0,1))$ such that $u \in
W^{1,p}_{\mathrm{loc}}(B(0,1))$ for every $p < \infty$, $u$ satisfies $\Div (A
\nabla u)=0$ with $A$ continuous but $u \not \in W^{1,
\infty}_{\mathrm{loc}}(B(0,1))$.
