Green Function in Metric Measure Spaces

Authors

Mario Bonk
Luca Capogna, Smith CollegeFollow
Xiaodan Zhou

Document Type

Article

Publication Date

4-19-2024

Abstract

We study existence and uniqueness of Green functions for the Cheeger QLaplacian in metric measure spaces that are Ahlfors Q-regular and support a Q-Poincar´e 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].

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights

Licensed to Smith College and distributed CC-BY 4.0 under the Smith College Faculty Open Access Policy.

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Bonk, Mario; Capogna, Luca; and Zhou, Xiaodan, "Green Function in Metric Measure Spaces" (2024). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/181