论文标题
在穆拉特紧凑性结果和应用的分数版本上
On a Fractional Version of a Murat Compactness Result and Applications
论文作者
论文摘要
本文为穆拉特和布雷兹斯的经典结果提供了扩展的分数sobolev sobolev空间，该结果指出，每一个$ h^{ - 1}（ - 1}（ω）$中的元素的正锥（ω）$将$ w^{ - 1，q}（ω）$固定在$ w^{-1，q}（ω）$中，适用于$ q <2 $，对于$ q <2 $，对于任何$ q <2 $，以及与lipc $之间的lips $之间。特别是，我们的证明包含经典结果。在我们的主要结果证明过程中开发了几种新的分析工具，这引起了更广泛的兴趣。随后，我们将结果应用于凸组的收敛性，并建立了Boccardo和Murat的MOSCO收敛结果的分数版本。最后，我们将此结果应用于准级别的不平等现象。
The paper provides an extension, to fractional order Sobolev spaces, of the classical result of Murat and Brezis which states that the positive cone of elements in $H^{-1}(Ω)$ compactly embeds in $W^{-1,q}(Ω)$, for every $q < 2$ and for any open and bounded set $Ω$ with Lipschitz boundary. In particular, our proof contains the classical result. Several new analysis tools are developed during the course of the proof to our main result which are of wider interest. Subsequently, we apply our results to the convergence of convex sets and establish a fractional version of the Mosco convergence result of Boccardo and Murat. We conclude with an application of this result to quasi-variational inequalities.
