Density of 0-homogeneous functions in $H^1(\partial \Omega)$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T05:50:25Z http://mathoverflow.net/feeds/question/95517 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95517/density-of-0-homogeneous-functions-in-h1-partial-omega Density of 0-homogeneous functions in $H^1(\partial \Omega)$ Josh 2012-04-29T19:37:40Z 2012-05-01T21:13:47Z <p><strong>Recall:</strong> A function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is called $0$-homogeneous if $f(\lambda x)= f(x)$ for every $\lambda>0$ and every $x\in \mathbb{R}^n$.</p> <p><strong>Question:</strong> Let $B$ a convex balanced and absorbent bounded domain of $\mathbb{R}^n$. Is the space of $0$-homogeneous $C^\infty(\mathbb{R}^n\setminus{0})$ functions dense in $H^1(\partial B)$?</p>