Plurisubharmonic functions with discontinuous boundary behavior
We study the Dirichlet problem for the complex Monge–Amp`ereoperator with bounded, discontinuous boundary data. If the set of discontinuities is b-pluripolar and the domain is B-regular, we are able to prove existence, uniqueness and some regularity estimates for a large class of complexMonge–Amp`ere measures. This result is optimal in the unit disk, as boundaryfunctions with b-pluripolar disconti
