The Journal of Geometric Analysis

, Volume 9, Issue 3, pp 491–511

Extension of smooth functions from finitely connected planar domains

Article

Abstract

Consider the Sobolev space Wk(Ω) of functions with bounded kth derivatives defined in a planar domain. We study the problem of extendability of functions from Wk(Ω) to the whole ℝ2 with preservation of class, i.e., surjectivity of the restriction operator Wk(ℝ2) → Wk(Ω).

Math Subject Classifications

46E35 

Key Words and Phrases

extension of smooth functions Whitney’s theorem intrinsic metric 

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Copyright information

© Mathematica Josephina, Inc. 1999

Authors and Affiliations

  1. 1.Department of MathematicsCollege of William and MaryWilliamsburg

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