论文标题
公制度量空间中的绿色功能
Green function in metric measure spaces
论文作者
论文摘要
我们研究了Cheeger $ Q $ -laplacian的绿色功能的存在和唯一度量的公制度量空间，这些空间是Ahlfors $ Q $ regular的，并支持$ Q $-Poincaré不平等，$ Q> 1 $。在相对紧凑的域和全局（无限）情况下，我们证明了绿色功能的独特性。我们还证明了无限空间中的全球绿色功能的存在，并在[BBL20]中证明了相对紧凑的域中现有结果。
We study existence and uniqueness of Green functions for the Cheeger $Q$-Laplacian in metric measure spaces that are Ahlfors $Q$-regular and support a $Q$-Poincaré inequality with $Q>1$. We prove uniqueness of Green functions both in the case of relatively compact domains, and in the global (unbounded) case. We also prove existence of global Green functions in unbounded spaces, complementing the existing results in relatively compact domains proved recently in [BBL20].
