Fractional Korn and Hardy-type inequalities for vector fields in half space
Fractional Korn and Hardy-type inequalities for vector fields in half space
复制标题
半空间向量场的分数式 Korn 和 Hardy 型不等式
DOI：
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发表时间：
2018
影响因子：
1.6
通讯作者：
T. Mengesha
中科院分区：
文献类型：
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作者：
T. Mengesha
基于一个修正的分数阶半范数，证明了半空间上向量场的一个分数阶Hardy型不等式。先验地，修改的半范数并不等同于标准的分数半范数，实际上给出了一个更小的范数。因此，我们证明的不等式改进了经典的向量场的分数阶哈代不等式。我们将使用不等式来建立定义在半空间上的函数空间（感兴趣的）与经典分数Sobolev空间的等价性，这相当于证明经典Korn不等式的分数版本。
We prove a fractional Hardy-type inequality for vector fields over the half space based on a modified fractional semi-norm. A priori, the modified semi-norm is not known to be equivalent to the standard fractional semi-norm and in fact gives a smaller norm, in general. As such, the inequality we prove improves the classical fractional Hardy inequality for vector fields. We will use the inequality to establish the equivalence of a space of functions (of interest) defined over the half space with the classical fractional Sobolev spaces, which amounts to prove a fractional version of the classical Korn’s inequality.