黎曼流形上的弱协变微分与Sobolev空间

Weak covariant differentiation and Sobolev space on Riemannian manifolds

在黎曼流形上引入了函数和协变张量场的弱协变微分,建立了广义散度概念。利用弱协变微分方法定义了黎曼流形上的Sobolev空间,并证明了它与现有定义的等价性。

The concept of weak covariant diifferentiation of function and tensor field is introduced; The generalized divergence of a vector field is established; and a characteristic of Sobolev spaces on Riemannian manifolds by means of weak covariant differentiation is given.