## Abstract

We provide an integral estimate for a non-divergence (non-variational) form second order elliptic equation aijuij=up, u≥0, p∈[0,1), with bounded discontinuous coefficients aij having small BMO norm. We consider the simplest discontinuity of the form~x⊗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~aij(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.

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.

Original language | English |
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Number of pages | 13 |

Publication status | Published - 11 Jan 2017 |