Work

Green function in metric measure spaces

Year: 2022

Type: preprint

Abstract: 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].

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2211.11974

Authors: Bonk, Mario, Capogna, Luca, Zhou, Xiaodan

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Japan Society for the Promotion of Science

Awards: Dynamics and Quasiconformal Geometry, Applications of Quasiconformal Geometry and Partial Differential Equations, Quasiconformal and Sobolev mappings on metric measure spaces

OpenAlex ID: W4309869958

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