From: "Gunter Bengel" <bengel@uni-muenster.de>
Subject: Re: Sobolev spaces
Date: 16 Jun 1999 15:30:01 -0500
Newsgroups: sci.math.research
Keywords: H=W theorem (Myers and Serrin) on density of Sobolev spaces

Antoni Zochowski <zochowsk@ibspan.waw.pl> writes:

> Under which conditions on the domain is H^2 dense in H^1 ?
> I mean here (if applicable) something weaker than
> the usual ones (cone condition, segment property etc.)
> 
> A.Zochowski
> zochowsk@ibspan.waw.pl

By the theorem of Myers and Serrin also known as "H = W" 
C^\infty \intersection  W^(m,p) is dense in W^(m,p) for p < \infty
without any hypothesis on the open set \Omega. You will find a proof
in Adams' book on Sobolev-Spaces or in "Gilbarg - Trudinger, Elliptic
PDE of Second Order" (Thm,7.9)

Gunter