  We study the mean values sets of the second order divergence form elliptic
operator with principal coefficients defined as $$a^{ij}_k(x):= \begin{cases}
\alpha_k \delta^{ij}(x) &x_n>0 \beta_k \delta^{ij}(x) &x_n<0. \end{cases}$$ In
particular, we will show that the mean value sets associated to such an
operator need not be convex as $\alpha_k$ and $\beta_k$ converge to 1. This
example then leads to an example of nonconvex mean value sets for smooth
$a^{ij}(x)$.
