论文标题
关于临界维度的浓度紧凑原理的评论
A remark on the concentration compactness principle in critical dimension
论文作者
论文摘要
我们证明了Sobolev Space的浓度紧凑原理的一些改进，$ W^{1，N} $在平滑的紧凑型Riemannian dimension $ n $上。作为一个应用程序，我们将Aubin定理扩展到$ \ Mathbb {s}^{n} $上，该区域元素的零一阶矩量为较高阶矩案例。我们的参数非常灵活，可以轻松修改以满足各种边界条件或属于高阶Sobolev空间的功能。
We prove some refinements of concentration compactness principle for Sobolev space $W^{1,n}$ on a smooth compact Riemannian manifold of dimension $n$. As an application, we extend Aubin's theorem for functions on $\mathbb{S}^{n}$ with zero first order moments of the area element to higher order moments case. Our arguments are very flexible and can be easily modified for functions satisfying various boundary conditions or belonging to higher order Sobolev spaces.
