Abstract

Let V be a complex variety in a bounded domain D in Cn. We are interested in finding sufficient conditions on V so that plurisubharmonic functions which are bounded from above on V can be approximated from above by continuous functions on V¯¯¯¯ and plurisubharmonic on V. Next, we discuss the possibility to extend a given real valued continuous function on ∂V to a maximal plurisubharmonic on V which is continuous up to the boundary.