度量空间中有界变差函数的迹定理
Trace theorems for functions of bounded variation in metric spaces
摘要：
本文证明了在度量测度空间中具有支持$1$不等式的加倍测度的某类域的边界上有界变差函数迹的存在性，并得到了迹函数的$L^1$估计.与其他论文中关于这个问题的痕迹的治疗相比，我们认为痕迹不需要在域的外部的函数的知识。对于在正容量集上为零的有界变差函数，我们也建立了一个Maz'ya型不等式。
英文摘要：
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 $1$-Poincaré 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.
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