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articleNo Access
THE DIRICHLET PROBLEM FOR MAXIMAL PLURISUBHARMONIC FUNCTIONS ON ANALYTIC VARIETIES IN ℂⁿ
- FRANK WIKSTRÖM
International Journal of Mathematics01 Apr 2009
Preview Abstract
Let Ω be a B-regular domain in ℂⁿ and let V be a locally irreducible analytic variety in Ω. Given a continuous function , we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by ϕ and furthermore that u is continuous on .
articleNo Access
Quasibounded plurisubharmonic functions
- Mårten Nilsson and
- Frank Wikström
International Journal of Mathematics03 Jul 2021
Preview Abstract
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 Dirichlet problems with unbounded boundary data admit unique solutions, and that these solutions are continuous outside a pluripolar set.

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