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We consider the Cauchy problem for semilinear parabolic equation indivergence form with obstacle. We show that under natural conditions on theright-hand side of the equation and mild conditions on the obstacle the problemhas a unique solution and we provide its stochastic representation in terms ofreflected backward stochastic differential equations. We prove also regularityproperties and approximation results for solutions of the problem.

Reflected BSDEs and obstacle problem for semilinear PDEs in divergence form