Uniform harmonic approximation of bounded functions

Gardiner, Stephen

doi:10.1090/S0002-9947-96-01455-9

Uniform harmonic approximation of bounded functions
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by Stephen J. Gardiner PDF

Trans. Amer. Math. Soc. 348 (1996), 251-265 Request permission

Abstract:

Let $\Omega$ be an open set in $\mathbb R^n$ and $E$ be a relatively closed subset of $\Omega$. We characterize those pairs $(\Omega ,E)$ which have the following property: every function which is bounded and continuous on $E$ and harmonic on $E^0$ can be uniformly approximated by functions harmonic on $\Omega$. Several related results concerning both harmonic and superharmonic approximation are also established.

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