A note for W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929382978748416 |
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| author | Tian, Yulu Zhao, Liang |
| author_facet | Tian, Yulu Zhao, Liang |
| contents | In this paper, we investigate the Sobolev spaces W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph G=(V,E), which are fundamental tools when we apply the variational methods to partial differential equations on graphs. As a key contribution of this note, we show that in general, W^{1,p}(V) is not equivalent to W_0^{1,p}(V) on locally finite graphs, which is different from the situation on Euclidean space R^N. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note for W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph Tian, Yulu Zhao, Liang Analysis of PDEs 46E39, 35P05, 05C63, 35R02, 35A15 In this paper, we investigate the Sobolev spaces W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph G=(V,E), which are fundamental tools when we apply the variational methods to partial differential equations on graphs. As a key contribution of this note, we show that in general, W^{1,p}(V) is not equivalent to W_0^{1,p}(V) on locally finite graphs, which is different from the situation on Euclidean space R^N. |
| title | A note for W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph |
| topic | Analysis of PDEs 46E39, 35P05, 05C63, 35R02, 35A15 |
| url | https://arxiv.org/abs/2406.08053 |