论文标题
Sobolev空间中径向对称函数的子空间的表征
A characterization of the subspace of radially symmetric functions in Sobolev spaces
论文作者
论文摘要
在本文中，我们表明，径向对称函数的非负整数顺序的任何Sobolev标准都等于其径向轮廓的加权Sobolev Norm。这是在径向Sobolev空间的完整表征上以加权的Sobolev空间来建立的，直到现在。作为应用程序，我们对旋转图的Sobolev规范进行了描述。
In this paper, we show that any Sobolev norm of nonnegative integer order of radially symmetric functions is equivalent to a weighted Sobolev norm of their radial profile. This establishes in terms of weighted Sobolev spaces on an interval a complete characterization of radial Sobolev spaces, which was open until now. As an application, we give a description of Sobolev norms of corotational maps.
