Trace inequality for $BV(\mathrm{\Omega })$ in smooth domains

This work is devoted to prove an optimum version of the trace inequality associated to the embedding $BV(\mathrm{\Omega })\subset L^1(\mathrm{\partial }\mathrm{\Omega })$. Special emphasis is placed on the regularity that the domain $\mathrm{\Omega }$ should exhibit for this result to be valid.