Closed BV-extension and $W^{1,1}$-extension sets
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916657898717184 |
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| author | Caputo, Emanuele Koivu, Jesse Lučić, Danka Rajala, Tapio |
| author_facet | Caputo, Emanuele Koivu, Jesse Lučić, Danka Rajala, Tapio |
| contents | This paper studies the relations between extendability of different classes of Sobolev $W^{1,1}$ and $BV$ functions from closed sets in general metric measure spaces. Under the assumption that the metric measure space satisfies a weak $(1,1)$-Poincaré inequality and measure doubling, we prove further properties for the extension sets. In the case of the Euclidean plane, we show that compact finitely connected $BV$-extension sets are always also $W^{1,1}$-extension sets. This is shown via a local quasiconvexity result for the complement of the extension set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed BV-extension and $W^{1,1}$-extension sets Caputo, Emanuele Koivu, Jesse Lučić, Danka Rajala, Tapio Metric Geometry Analysis of PDEs Functional Analysis 30L99, 46E35, 26B30 This paper studies the relations between extendability of different classes of Sobolev $W^{1,1}$ and $BV$ functions from closed sets in general metric measure spaces. Under the assumption that the metric measure space satisfies a weak $(1,1)$-Poincaré inequality and measure doubling, we prove further properties for the extension sets. In the case of the Euclidean plane, we show that compact finitely connected $BV$-extension sets are always also $W^{1,1}$-extension sets. This is shown via a local quasiconvexity result for the complement of the extension set. |
| title | Closed BV-extension and $W^{1,1}$-extension sets |
| topic | Metric Geometry Analysis of PDEs Functional Analysis 30L99, 46E35, 26B30 |
| url | https://arxiv.org/abs/2503.15716 |