Abstract
We consider the obstacle problem with two irregular barriers for the Cauchy–Dirichlet problem for semilinear parabolic equations with measure data. We prove the existence and uniqueness of renormalized solutions of the problem as well as results on approximation of the solutions by the penalization method. In the proofs, we use probabilistic methods of the theory of Markov processes and the theory of backward stochastic differential equations.
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Klimsiak, T., Rozkosz, A. Obstacle problem for semilinear parabolic equations with measure data. J. Evol. Equ. 15, 457–491 (2015). https://doi.org/10.1007/s00028-014-0269-8
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DOI: https://doi.org/10.1007/s00028-014-0269-8