Green function in metric measure spaces
Analysis of PDEs
2024-04-22 v3 Metric Geometry
Abstract
We study existence and uniqueness of Green functions for the Cheeger -Laplacian in metric measure spaces that are Ahlfors -regular and support a -Poincar\'e inequality with . 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].
Cite
@article{arxiv.2211.11974,
title = {Green function in metric measure spaces},
author = {Mario Bonk and Luca Capogna and Xiaodan Zhou},
journal= {arXiv preprint arXiv:2211.11974},
year = {2024}
}
Comments
This new version of the paper includes the case 1<Q<2 for the uniqueness of the global Green function. We have also edited the acknowledgments