7 citations · 7 across the 6 of their papers we have counts for
6 papers · 1 filter
On the size of boundary pluripolar sets
Mårten Nilsson
We prove a number of results related to the size and propagation of boundary pluripolar sets, the exceptional sets for the Dirichlet problem for the complex Monge--Ampère equation.…
Quasibounded solutions to the complex Monge-Ampère equation
Mårten Nilsson
We study the Dirichlet problem for the complex Monge-Ampère operator on a B-regular domain , allowing boundary data that is singular or unbounded. We introduce the concept of pl…
Variations on a theorem by Edwards
Mårten Nilsson, Frank Wikström
We discuss two variations of Edwards' duality theorem. More precisely, we prove one version of the theorem for cones not necessarily containing all constant functions. In particula…
Plurisubharmonic functions with discontinuous boundary behavior
Mårten Nilsson
We study the Dirichlet problem for the complex Monge-Ampère operator with bounded, discontinuous boundary data. If the set of discontinuities is b-pluripolar and the domain is B-re…
Continuity of envelopes of unbounded plurisubharmonic functions
Mårten Nilsson
On bounded B-regular domains, we study envelopes of plurisubharmonic functions bounded from above by a function such that on the closure of the domain. For satisf…
Quasibounded plurisubharmonic functions
Mårten Nilsson, Frank Wikström
We extend the notion of quasibounded harmonic functions to the plurisubharmonic setting. As an application, using the theory of Jensen measures, we show that certain generalized Di…