论文标题
Bourgain-Brezis-Mironescu对Sobolev空间的表征
A Remake of Bourgain-Brezis-Mironescu Characterization of Sobolev Spaces
论文作者
论文摘要
我们介绍了一大类集中的$ p $lévy的集成函数，这些功能近似于统一，这是我们提供的sobolev空间非局部表征以及通过非局部能量形式的界限变化函数空间的核心工具。事实证明，这种非局部表征是在满足扩展特性的域上定义Sobolev空间的必要和足够标准。我们还研究了扩展属性不一定拥有的一般情况。在后一种情况下，我们建立了涉及分布梯度引起的局部ra量测量的非局部ra量测量的弱收敛性。
We introduce a large class of concentrated $p$-Lévy integrable functions approximating the unity, which serves as the core tool from which we provide a nonlocal characterization of Sobolev spaces and the space of functions of bounded variation via nonlocal energies forms. It turns out that this nonlocal characterization is a necessary and sufficient criterion to define Sobolev spaces on domains satisfying the extension property. We also examine the general case where the extension property does not necessarily hold. In the latter case, we establish weak convergence of the nonlocal Radon measures involved to the local Radon measures induced by the distributional gradient.
