Approximation of m-subharmonic functions on bounded domains in Cn

Let D be a bounded domain in Cn. We study approximation of (not necessarily bounded from above) m-subharmonic function D by continuous m-subharmonic ones defined on neighborhoods of D‾. We also consider the existence of a m-subharmonic function on D whose boundary values coincides with a given real valued continuous function on ∂D except for a sufficiently small subset of ∂D.