  It is known that solutions to second order uniformly elliptic and parabolic
equations, either in divergence or nondivergence (general) form, are H\"{o}lder
continuous and satisfy the interior Harnack inequality. We show that even in
the one-dimensional case ($x\in R^1$), these properties are not preserved for
equations of mixed divergence-nondivergence structure: for elliptic equations.
\begin{equation*}
  D_i(a^1_{ij}D_ju)+a^2_{ij}D_{ij}u=0, \end{equation*} and parabolic equations
\begin{equation*} p\partial_t u=D_i(a_{ij}D_ju), \end{equation*} where
$p=p(t,x)$ is a bounded strictly positive function. The H\"{o}lder continuity
and Harnack inequality are known if $p$ does not depend either on $t$ or on
$x$. We essentially use homogenization techniques in our construction.
Bibliography: 23 titles.
