Bilateral inequalities and implicit unilateral systems of the non-variational type

We prove that ageneralized solution exists for a bilateral problem relative to second order linear elliptic operator with principal part not in divergence form. We also prove that this solution isregular, when the obstacles are sufficiently regular, and that it provides an appropriate substitute for the solution when the hypotheses of regularity are not satisfied. A probabilistic characterization of this solution is also given.