Arkiv för Matematik

  • Ark. Mat.
  • Volume 55, Number 1 (2017), 229-241.

A note on approximation of plurisubharmonic functions

Håkan Persson and Jan Wiegerinck

Full-text: Open access

Abstract

We extend a recent result of Avelin, Hed, and Persson about approximation of functions $f$ that are plurisubharmonic on a domain $\Omega$ and continuous on $\overline{\Omega}$, with functions that are plurisubharmonic on (shrinking) neighborhoods of $\overline{\Omega}$. We show that such approximation is possible if the boundary of $\Omega$ is $C^0$ outside a countable exceptional set $E \subset \partial \Omega$. In particular, approximation is possible on the Hartogs triangle. For Hölder continuous $u$, approximation is possible under less restrictive conditions on $E$. We next give examples of domains where this kind of approximation is not possible, even when approximation in the Hölder continuous case is possible.

Article information

Source
Ark. Mat., Volume 55, Number 1 (2017), 229-241.

Dates
Received: 5 October 2016
Revised: 27 January 2017
First available in Project Euclid: 2 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.afm/1517535611

Digital Object Identifier
doi:10.4310/ARKIV.2017.v55.n1.a12

Mathematical Reviews number (MathSciNet)
MR3711151

Zentralblatt MATH identifier
06823282

Subjects
Primary: 32U05: Plurisubharmonic functions and generalizations [See also 31C10]
Secondary: 31B05: Harmonic, subharmonic, superharmonic functions 31B25: Boundary behavior

Keywords
plurisubharmonic function approximation Mergelyan type approximation

Citation

Persson, Håkan; Wiegerinck, Jan. A note on approximation of plurisubharmonic functions. Ark. Mat. 55 (2017), no. 1, 229--241. doi:10.4310/ARKIV.2017.v55.n1.a12. https://projecteuclid.org/euclid.afm/1517535611


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