= Bounded BV extension operator
{title2=$E:BV(\Omega)\to BV(\mathbb R^n),\quad\|Eu\|_{BV}\le C_\Omega\|u\|_{BV}$}
For a bounded <Lipschitz domain>, functions can be extended with the displayed bound and common <compact support>. Reflect across local Lipschitz boundary graphs, combine the reflected functions with a <partition of unity>, and multiply by a fixed <cutoff function>. Lipschitz coordinate changes control <derivative> <measures>; the product rule bounds <cutoff function> terms by the $L^1$ <norm>. Zero extension is also possible with an estimate for <BV traces on a hypersurface>, but its boundary jump must be included in the variation.
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