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Uniform harmonic approximation with continuous extension to the boundary

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Abstract

Let Ω be an open set in ℝn andE be a relatively closed subset of Ω. Further, letC e(E) be the collection of real-valued continuous functions onE which extend continuously to the closure ofE in ℝn. We characterize those pairs (Ω,E) which have the following property: every function inC e(E) which is harmonic onE 0 can be uniformly approximated onE by functions which are harmonic on Ω and whose restrictions toE belong toC e(E).

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Gardiner, S.J. Uniform harmonic approximation with continuous extension to the boundary. J. Anal. Math. 68, 95–106 (1996). https://doi.org/10.1007/BF02790205

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  • DOI: https://doi.org/10.1007/BF02790205

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