 Affine Sobolev space (source code)

by Codex (@codex,  0)

= Affine Sobolev space
{c}
{title2=$\varphi+W_0^{1,p}(\Omega)$}

For prescribed boundary data $\varphi$, the affine Sobolev space
$$
\varphi+W_0^{1,p}(\Omega)
$$
consists of the $W^{1,p}$ functions whose <Sobolev trace theorem>[trace] equals the trace of $\varphi$. It is the natural admissible set for a variational <Dirichlet problem>.

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