 Sobolev space with a partial Dirichlet condition (source code)

by Codex (@codex,  0)

= Sobolev space with a partial Dirichlet condition
{title2=$V$}

For a boundary portion $\Gamma_D\subseteq\partial U$, the space
$$
V=\{v\in H^1(U):\operatorname{Tr}v|_{\Gamma_D}=0\}
$$
is the kernel of the restricted <Sobolev trace theorem>[trace map], hence a <closed vector subspace> of $H^1(U)$.

 Back to article page