Continuity of envelopes of unbounded plurisubharmonic functions
(2022) In Mathematische Zeitschrift 301(4). p.3959-3971- Abstract
On bounded B-regular domains, we study envelopes of plurisubharmonic functions bounded from above by a function ϕ which is continuous in the extended reals on the closure of the domain. For ϕ satisfying certain additional criteria limiting its behavior at the singularities, we establish a set where the Perron–Bremermann envelope Pϕ is guaranteed to be continuous. This result is a generalization of a classic result in pluripotential theory due to J. B. Walsh. As an application, we show that the complex Monge–Ampère equation (ddcu)n=μbeing uniquely solvable for continuous boundary data implies that it is also uniquely solvable for a class of boundary values continuous in the extended reals and unbounded from above.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4d65ba9f-7b49-4a07-bde4-f3a4be0613b6
- author
- Nilsson, Mårten LU
- organization
- publishing date
- 2022-08
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Mathematische Zeitschrift
- volume
- 301
- issue
- 4
- pages
- 13 pages
- publisher
- Springer
- external identifiers
-
- scopus:85130699542
- ISSN
- 0025-5874
- DOI
- 10.1007/s00209-022-03043-2
- project
- Boundary singularities of plurisubharmonic functions
- language
- English
- LU publication?
- yes
- id
- 4d65ba9f-7b49-4a07-bde4-f3a4be0613b6
- date added to LUP
- 2022-12-27 15:58:12
- date last changed
- 2025-04-04 14:02:33
@article{4d65ba9f-7b49-4a07-bde4-f3a4be0613b6,
abstract = {{<p>On bounded B-regular domains, we study envelopes of plurisubharmonic functions bounded from above by a function ϕ which is continuous in the extended reals on the closure of the domain. For ϕ satisfying certain additional criteria limiting its behavior at the singularities, we establish a set where the Perron–Bremermann envelope Pϕ is guaranteed to be continuous. This result is a generalization of a classic result in pluripotential theory due to J. B. Walsh. As an application, we show that the complex Monge–Ampère equation (ddcu)n=μbeing uniquely solvable for continuous boundary data implies that it is also uniquely solvable for a class of boundary values continuous in the extended reals and unbounded from above.</p>}},
author = {{Nilsson, Mårten}},
issn = {{0025-5874}},
language = {{eng}},
number = {{4}},
pages = {{3959--3971}},
publisher = {{Springer}},
series = {{Mathematische Zeitschrift}},
title = {{Continuity of envelopes of unbounded plurisubharmonic functions}},
url = {{http://dx.doi.org/10.1007/s00209-022-03043-2}},
doi = {{10.1007/s00209-022-03043-2}},
volume = {{301}},
year = {{2022}},
}