Trace and extension theorems for functions of bounded variation
Trace and extension theorems for functions of bounded variation
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有界变分函数的迹定理和可拓定理
DOI：
10.2422/2036-2145.201511_007
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Marie A. Snipes
中科院分区：
文献类型：
--
作者：
Luk'avs Mal'y;N. Shanmugalingam;Marie A. Snipes
本文证明了：当$\Omega$是二重度量测度空间中具有正则边界$\partial\Omega$的区域时，$\Omega$上的每一个$L^1$-可积函数都可以作为$\Omega$上有界变差函数的迹得到.特别地，$BV（\Omega）$的迹类是$L^1（\partial\Omega）$，前提是$\Omega$支持1-Poincar\'e不等式。我们还构造了一个从Besov函数类到BV（\Omega）的有界线性扩张。
In this paper we show that every $L^1$-integrable function on $\partial\Omega$ can be obtained as the trace of a function of bounded variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary $\partial\Omega$ in a doubling metric measure space. In particular, the trace class of $BV(\Omega)$ is $L^1(\partial\Omega)$ provided that $\Omega$ supports a 1-Poincar\'e inequality. We also construct a bounded linear extension from a Besov class of functions on $\partial\Omega$ to $BV(\Omega)$.