Local Sobolev space
= Local Sobolev space
{c}
{title2=$H^s_{\mathrm{loc}}(X)$}
A distribution $u$ on an open set $X$ belongs to $H^s_{\mathrm{loc}}(X)$ when $\chi u\in H^s(\mathbb R^n)$ for every test function $\chi\in C_c^\infty(X)$.
= Local Sobolev space
{c}
{title2=$H^s_{\mathrm{loc}}(X)$}
A distribution $u$ on an open set $X$ belongs to $H^s_{\mathrm{loc}}(X)$ when $\chi u\in H^s(\mathbb R^n)$ for every test function $\chi\in C_c^\infty(X)$.