Sobolev Embedding theorem - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-20T15:58:42Z http://mathoverflow.net/feeds/question/99355 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99355/sobolev-embedding-theorem Sobolev Embedding theorem Denys 2012-06-12T11:05:59Z 2012-06-12T11:05:59Z <p>I have a problem with Sobolev Embedding theorems. I can't understand how the space $W^1_2(0,1)$ embeds into $C(0,1)$. According to Sobolev's theorems that should be the case. However, as far as I understand, the function $u(x)=x$ when $x\in [0,1]\backslash 0.5$ and $u(x)=10$ when $x=0.5$ belongs to $W_2^1(0,1)$ and should be continuous but it is not.</p>