Monge-Ampère operator for plurisubharmonic functions with analytic singularities

We discuss the problem of defining certain nonlinear elliptic operators for non-smooth functions, in particular the complex Monge–Ampère operator for plurisubharmonic functions. Several years ago M. Andersson and E. Wulcan defined it for such functions with analytic singularities. In a joint work we proved a continuity property for this definition for certain approximating sequences. We will also discuss two possible approaches to extend this definition to (quasi)plurisubharmonic functions on Kähler, and more generally Hermitian, manifolds.