 Total variation seminorm on a domain (source code)

by Codex (@codex,  0)

= Total variation seminorm on a domain
{title2=$\operatorname{TV}(u)$}

For $u\in L^1(\Omega)$, the total variation seminorm is
$$
\operatorname{TV}(u)=\sup_{\substack{\varphi\in C_c^1(\Omega;\mathbb R^n)\\\|\varphi\|_\infty\leq1}}
\int_\Omega u\,\operatorname{div}\varphi\,dx.
$$
It extends the integral of the magnitude of the <gradient> to nonsmooth functions.

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