On a \(p(t,x)\)-Laplace evolution equation with a stochastic force (Q378039)

This paper studies the stochastic perturbation of a nonlinear singular/degenerated parabolic problem with a \(p\)-Laplacian, where \(p\) depends on space and time. Since Orlicz type spaces do not fit into the classical framework of Bochner spaces, the authors have to adapt classical methods based on monotonicity arguments. For the proof of existence, the authors study a regularization with a \(q\)-Laplacian for sufficiently large \(q\) and uniform estimates derived via Itô's formula.