Superharmonic extension and harmonic approximation

Gardiner, Stephen J.

Annales de l'Institut Fourier, Tome 44 (1994), p. 65-91 / Harvested from Numdam

Résumé

Soient $\Omega $ un ouvert de ${\Bbb R}^n$ et $E$ une partie de $\Omega $. Nous caractérisons les paires $(\Omega , E)$ qui nous permettent d’étendre les fonctions surharmoniques de $E$ à $\Omega $, ou d’approcher les fonctions sur $E$ par les fonctions harmoniques sur $\Omega $.

Abstract

Let $\Omega $ be an open set in ${\Bbb R}^n$ and $E$ be a subset of $\Omega $. We characterize those pairs $(\Omega , E)$ which permit the extension of superharmonic functions from $E$ to $\Omega $, or the approximation of functions on $E$ by harmonic functions on $\Omega $.

Détail

Publié le : 1994-01-01

MR 95a:31006 | Zbl 0795.31004

DOI : https://doi.org/10.5802/aif.1389

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