论文标题
Sobolev空间上的组成操作员的几何理论
Geometric theory of composition operators on Sobolev spaces
论文作者
论文摘要
在本文中，我们介绍了Sobolev空间上构图操作员几何理论的基本概念。该理论的主要对象是拓扑映射，通过组成规则在Sobolev空间上生成有限的嵌入操作员。从某种意义上说，这一理论是对准文献映射理论的“概括”，但组成操作者的理论将其应用于嵌入sobolev嵌入定理的应用，椭圆运算符的光谱理论和连续机械问题。
In this paper, we present the basic concepts of the geometric theory of composition operators on Sobolev spaces. The main objects of the theory are topological mappings which generate bounded embedding operators on Sobolev spaces by the composition rule. This theory is in some sense a "generalization" of the theory of quasiconformal mappings, but the theory of composition operators is oriented to its applications to the Sobolev embedding theorems, the spectral theory of elliptic operators and continuum mechanics problems.
