Green function in metric measure spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910414828208128 |
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| author | Bonk, Mario Capogna, Luca Zhou, Xiaodan |
| author_facet | Bonk, Mario Capogna, Luca Zhou, Xiaodan |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_11974 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Green function in metric measure spaces Bonk, Mario Capogna, Luca Zhou, Xiaodan Analysis of PDEs Metric Geometry 30L99, 31C15, 35J92 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]. |
| title | Green function in metric measure spaces |
| topic | Analysis of PDEs Metric Geometry 30L99, 31C15, 35J92 |
| url | https://arxiv.org/abs/2211.11974 |