Nonlocal criteria for compactness in the space of $L^{p}$ vector fields
Nonlocal criteria for compactness in the space of $L^{p}$ vector fields
复制标题
$L^{p}$ 向量场空间中的紧致性非局部准则
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Xiaochuan Tian
中科院分区：
文献类型：
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作者：
Q. Du;T. Mengesha;Xiaochuan Tian
本文给出了一组充分条件，保证了定义在$mathbb{R}^{d}$或$mathbb{R}^{d}$中的有界域上的$L^p$向量场的函数空间中的紧包含.该标准是非局部的，并给出相对于非局部相互作用内核，可能不一定是径向对称的。此外，向量场的这些准则也不同于标量场的那些准则，因为这些条件是基于只涉及向量场部分分量的非定域相互作用。
This work presents a set of sufficient conditions that guarantee a compact inclusion in the function space of $L^p$ vector fields defined on a domain that is either a bounded domain in $mathbb{R}^{d}$ or $mathbb{R}^{d}$ itself. The criteria are nonlocal and are given with respect to nonlocal interaction kernels that may not be necessarily radially symmetric. Moreover, these criteria for vector fields are also different from those given for scalar fields in that the conditions are based on nonlocal interactions involving only parts of the components of the vector fields.