奇异流形上的函数空间
Function Spaces on Singular Manifolds
摘要：
结果表明，在$\mathbb{R}^n$的有界光滑域上，Sobolev-Slobodeckii和Bessel势空间的大多数著名的基本结果在一类广泛的具有奇异性和边界的黎曼流形上继续有效，只要引入适当的权，它反映了奇异性的性质.这些结果对研究分段光滑区域上的偏微分方程具有重要意义。
英文摘要：
It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with singularities and boundary, provided suitable weights, which reflect the nature of the singularities, are introduced. These results are of importance for the study of partial differential equations on piece-wise smooth domains.
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