Maps of bounded variation from PI spaces to metric spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912517522980864 |
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| author | Brena, Camillo Nobili, Francesco Pasqualetto, Enrico |
| author_facet | Brena, Camillo Nobili, Francesco Pasqualetto, Enrico |
| contents | We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincaré property, we produce a well-behaved relaxation theory via approximation by simple maps. Moreover, several equivalent characterizations are given, including a notion in weak duality with test plans. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00768 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maps of bounded variation from PI spaces to metric spaces Brena, Camillo Nobili, Francesco Pasqualetto, Enrico Functional Analysis Analysis of PDEs Metric Geometry 53C23, 26A45, 26B30, 49J52, 30L99 We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincaré property, we produce a well-behaved relaxation theory via approximation by simple maps. Moreover, several equivalent characterizations are given, including a notion in weak duality with test plans. |
| title | Maps of bounded variation from PI spaces to metric spaces |
| topic | Functional Analysis Analysis of PDEs Metric Geometry 53C23, 26A45, 26B30, 49J52, 30L99 |
| url | https://arxiv.org/abs/2306.00768 |