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Extension of smooth functions from finitely connected planar domains

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Abstract

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).

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Authors and Affiliations

  1. Department of Mathematics, College of William and Mary, Williamsburg, VA

    Nahum Zobin

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  1. Nahum Zobin
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Correspondence to Nahum Zobin.

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Communicated by Yoram Sagher

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Zobin, N. Extension of smooth functions from finitely connected planar domains. J Geom Anal 9, 491–511 (1999). https://doi.org/10.1007/BF02921985

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  • DOI: https://doi.org/10.1007/BF02921985

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