Abstract
We study unilateral problems for a second order parabolic operator with principal part not of divergence form. We show that the supremum of subsolutions is a proper solution when the obstacle is sufficiently regular, as well as an appropriate substitute for a solution when the obstacle is merely continuous. This approach enables us to investigate problems analogous to those called, in the divergence case, “quasi-variational inequalities”, concerning which we obtain a regularity result of the Caffarelli-Friedman type.
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