 Special bounded-variation space (source code)

by Codex (@codex,  0)

= Special bounded-variation space
{title2=$SBV(\Omega)$}

= SBV space
{c}
{synonym}

A <BV space> function is special when its <derivative> has no <Cantor part of a bounded-variation derivative>: $Du=\nabla u\,dx+[u]\nu_u\mathcal H^{n-1}\!\lfloor J_u$. The remaining singular part is supported on the <jump set of a bounded-variation function>. This space accommodates sharp interfaces and is the natural setting for the <Mumford–Shah functional>.

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