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Quasibounded plurisubharmonic functions

Nilsson, Mårten LU and Wikström, Frank LU orcid (2021) In International Journal of Mathematics 32(9).
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.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
complex Monge-Ampère equation, Jensen measures, maximal plurisubharmonic functions, Pluripotential theory
in
International Journal of Mathematics
volume
32
issue
9
article number
2150068
publisher
World Scientific Publishing
external identifiers
  • scopus:85109385420
ISSN
0129-167X
DOI
10.1142/S0129167X21500683
project
Boundary singularities of plurisubharmonic functions
language
English
LU publication?
yes
id
33243402-e1d9-4e7f-935b-a66907674166
date added to LUP
2021-08-23 11:57:09
date last changed
2024-12-01 09:19:00
@article{33243402-e1d9-4e7f-935b-a66907674166,
  abstract     = {{<p>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.</p>}},
  author       = {{Nilsson, Mårten and Wikström, Frank}},
  issn         = {{0129-167X}},
  keywords     = {{complex Monge-Ampère equation; Jensen measures; maximal plurisubharmonic functions; Pluripotential theory}},
  language     = {{eng}},
  number       = {{9}},
  publisher    = {{World Scientific Publishing}},
  series       = {{International Journal of Mathematics}},
  title        = {{Quasibounded plurisubharmonic functions}},
  url          = {{http://dx.doi.org/10.1142/S0129167X21500683}},
  doi          = {{10.1142/S0129167X21500683}},
  volume       = {{32}},
  year         = {{2021}},
}