Obstacle problem for evolution equations involving measure data and operator corresponding to semi-Dirichlet form

Tomasz Klimsiak

Published 2016-12-21Version 1

In the paper we consider obstacle problem, with one and two irregular barriers, for semilinear evolution equation involving measure data and operator corresponding to semi-Dirichlet form. We prove the existence and uniquueness of solutions under the assumption that the right-hand side of the equation is monotone and satisfies mild integrability conditions. To treat the case of irregular barriers, we extend the theory of precise version of a function introduced by M. Pierre. We also give some applications to so-called switching problem.