Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces
Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces
复制标题
DOI：
10.1007/s002090100252
复制
发表时间：
2001-10
影响因子：
0.8
通讯作者：
K. Kuwae;Yoshiroh Machigashira;T. Shioya
中科院分区：
文献类型：
--
作者：
K. Kuwae;Yoshiroh Machigashira;T. Shioya
本文证明了Sobolev空间嵌入到Alexandrov空间的任何相对紧开子集的紧性。作为推论，由Dirichlet（能量）形式导出的生成元具有离散谱。生成元可以由Alexandrov空间上DC结构导出的Laplacian近似。我们还证明了局部Hölder连续热核的存在性。
We prove the compactness of the imbedding of the Sobolev spaceintofor any relatively compact open subsetof an Alexandrov space. As a corollary, the generator induced from the Dirichlet (energy) form has discrete spectrum. The generator can be approximated by the Laplacian induced from theDC-structure on the Alexandrov space. We also prove the existence of the locally Hölder continuous heat kernel.