Let $Q=(0,1)\times (0,1)$ and $u\in BV(Q)$ where $BV$ stands for bounded variation.
My question, is there exist a slice $S:=\{t\}\times (0,1)\subset Q$ such that $$ \|u\|_{BV(S)}\leq \|u\|_{BV(Q)}? $$
I know a similar result holds in sobolev space, so I am wondering is there a similar one hold in $BV$ space.