The Journal of Geometric Analysis

, Volume 9, Issue 3, pp 491–511

Extension of smooth functions from finitely connected planar domains


DOI: 10.1007/BF02921985

Cite this article as:
Zobin, N. J Geom Anal (1999) 9: 491. doi:10.1007/BF02921985


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


Key Words and Phrases

extension of smooth functionsWhitney’s theoremintrinsic metric

Copyright information

© Mathematica Josephina, Inc. 1999

Authors and Affiliations

  1. 1.Department of MathematicsCollege of William and MaryWilliamsburg