Superharmonic extension and harmonic approximation

Gardiner, Stephen J.

Annales de l'Institut Fourier, Tome 44 (1994) no. 1, pp. 65-91.

Soient $\Omega$ un ouvert de ${ℝ}^n$ 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 $\Omega$.

Let $\Omega$ be an open set in ${ℝ}^n$ 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 $\Omega$.

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