## Arkiv för Matematik

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

### A note on approximation of plurisubharmonic functions

#### 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
Revised: 27 January 2017
First available in Project Euclid: 2 February 2018

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

#### 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