We consider semilinear obstacle problem with measure data associated with uniformly elliptic divergence form operator. We prove existence and uniqueness of entropy solution of the problem and provide stochastic representation of the solution in terms of some generalized reflected backward stochastic differential equations with random terminal time.
"Stochastic representation of entropy solutions of semilinear elliptic obstacle problems with measure data." Electron. J. Probab. 17 1 - 27, 2012. https://doi.org/10.1214/EJP.v17-2062