论文标题
BV和Sobolev函数通过度量空间中的非局部功能的表征
A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces
论文作者
论文摘要
我们研究了BV和SOBOLEV函数的表征，该函数在配备了双重度量和支持庞加莱不平等的度量方面的非局部功能。与以前的工作相比，我们考虑更多的一般功能。我们还为$ p = 1 $进行反例，证明与欧几里得空间不同，在度量度量空间中，非局部函数的极限仅与变体度量$ \ |相当，而不一定是相等的。 df \ |（ω）$。
We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincaré inequality. Compared with previous works, we consider more general functionals. We also give a counterexample in the case $p=1$ demonstrating that unlike in Euclidean spaces, in metric measure spaces the limit of the nonlocal functions is only comparable, not necessarily equal, to the variation measure $\| Df\|(Ω)$.
