Inserted: 24 jul 2015
Last Updated: 19 jun 2018
Journal: J. Funct. Anal.
In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a $1$-Poincar\'e inequality, and obtain $L^1$ estimates of the trace functions. In contrast with the treatment of traces given in other papers on this subject, the traces we consider do not require knowledge of the function in the exterior of the domain. We also establish a Maz'ya-type inequality for functions of bounded variation that vanish on a set of positive capacity.
Keywords: BV functions, jump sets, traces, Whitney cover, discrete convolution