A Nonvariational Second Order Elliptic Operator with Singular Elliptic Measure

We exhibit an example which proves that the elliptic measure for a second-order operator of the form <!-- MATH $\Sigma _{i,j = 1}^n{a_{ij}}D_{ij}^2$ --> with continuous coefficients can be singular with respect to the surface measure on the boundary of a smooth two-dimensional domain.