  We provide an integral estimate for a non-divergence (non-variational) form
second order elliptic equation $a_{ij}u_{ij}=u^p$, $u\ge 0$, $p\in[0, 1)$, with
bounded discontinuous coefficients $a_{ij}$ having small BMO norm. We consider
the simplest discontinuity of the form~$x\otimes x|x|^{-2}$ at the origin. As
an application we show that the free boundary corresponding to the obstacle
problem (i.e. when~$p=0$) cannot be smooth at the points of discontinuity
of~$a_{ij}(x)$.
  To implement our construction, an integral estimate and a scale invariance
will provide the homogeneity of the blow-up sequences, which then can be
classified using ODE arguments.
