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Journal of Function Spaces and Applications
Volume 5, Issue 3, Pages 243-268
http://dx.doi.org/10.1155/2007/471535

Trace theorems for Sobolev-Slobodeckij spaces with or without weights

Doyoon Kim

Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, Ontario K1N 6N5, Canada

Received 1 April 2005

Academic Editor: Hans Triebel

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that the well-known trace theorem for weighted Sobolev spaces holds true under minimal regularity assumptions on the domain. Using this result, we prove the existence of a bounded linear right inverse of the trace operator for Sobolev-Slobodeckij spaces Wps(Ω) when s-1/p is an integer.