论文标题
关于分数订单的Sobolev规范的评论
Remarks on Sobolev norms of fractional orders
论文作者
论文摘要
当在Lipschitz域的适当子集中支持属于分数Sobolev空间的函数，该函数在其上定义了Sobolev空间时，其Sobolev Norm作为较小集合的函数与整个域的标准相比如何？比较常数依赖于什么？不同的规范行为有所不同吗？本文解决了这些问题。我们证明了一些不平等，并反驳了一些反例误解。
When a function belonging to a fractional-order Sobolev space is supported in a proper subset of the Lipschitz domain on which the Sobolev space is defined, how is its Sobolev norm as a function on the smaller set compared to its norm on the whole domain? On what do the comparison constants depend on? Do different norms behave differently? This article addresses these issues. We prove some inequalities and disprove some misconceptions by counter-examples.
