Extension of smooth functions from finitely connected planar domains
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Consider the Sobolev space W∞k(Ω) of functions with bounded kth derivatives defined in a planar domain. We study the problem of extendability of functions from W∞k(Ω) to the whole ℝ2 with preservation of class, i.e., surjectivity of the restriction operator W∞k(ℝ2) → W∞k(Ω).
Math Subject Classifications46E35
Key Words and Phrasesextension of smooth functions Whitney’s theorem intrinsic metric
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