From: "Gunter Bengel" 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 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