Obstacle problem for semilinear parabolic equations with measure data

Abstract

We consider the obstacle problem with two irregular reflecting 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 and well as results on approximation of the solutions by the penaliztion method. In the proofs we use probabilistic methods of the theory of Markov processes and the theory of backward stochastic differential equations.

References in corpus (3)

• Renormalized solutions of nonlinear parabolic equations with general measure data
• Diffuse measures and nonlinear parabolic equations
• Dirichlet forms and semilinear elliptic equations with measure data

Cited by in corpus (4)

• Renormalized solutions of semilinear equations involving measure data and operator corresponding to Dirichlet form
• Systems of semilinear parabolic variational inequalities with time-dependent convex obstacles
• Large time behaviour of solutions to parabolic equations with Dirichlet operators and nonlinear dependence on measure data
• Systems of BSDEs with oblique reflection and related optimal switching problems