Re: Sobolev spaces and counterexamples.

smnewberger_at_comcast.net
Date: 12/12/04 

Date: 11 Dec 2004 17:25:04 -0800

C^\infty(U)intersect W^(k,p)(U) is dense in W^(k,p) (U) || ||(k,p)
for any open set U,bounded or not . An reference is RA Adams and J
Fournier,
Sobelev Spaces 2nd edition Academic Press 2003, Chapter 3 pp 65-70 .If
U is bounded and the boundary has the segment condition (I believe that
includes C^1 boundaries but I never checked this) then c6\infty
functions on R^n with compact support restricted to U are dense and
these have bounded derivatives of all orders The convergence
restrictions about convergence in W^loc in Evens'wonderful book are
not needed .Regards,Stuart M Newberger

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