Uniform harmonic approximation with continuous extension to the boundary |
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Authors: | Stephen J Gardiner |
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Institution: | (1) Department of Mathematics, University College Dublin, Dublin 4, Ireland |
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Abstract: | Let Ω be an open set in ℝ
n
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 ℝ
n
. 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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Keywords: | |
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