Gradient flows of $(K,N)$-convex functions with negative $N$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916037398626304 |
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| author | Schiavo, Lorenzo Dello Magnabosco, Mattia Rigoni, Chiara |
| author_facet | Schiavo, Lorenzo Dello Magnabosco, Mattia Rigoni, Chiara |
| contents | We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaining as values both the positive and the negative infinity. We prove several properties of gradient flows of $(K,N)$-convex functionals characterized by Evolution Variational Inequalities, including contractivity, regularity, and uniqueness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient flows of $(K,N)$-convex functions with negative $N$ Schiavo, Lorenzo Dello Magnabosco, Mattia Rigoni, Chiara Functional Analysis Metric Geometry 49Q20 (Primary), 49J52, 53C23 (Secondary) We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaining as values both the positive and the negative infinity. We prove several properties of gradient flows of $(K,N)$-convex functionals characterized by Evolution Variational Inequalities, including contractivity, regularity, and uniqueness. |
| title | Gradient flows of $(K,N)$-convex functions with negative $N$ |
| topic | Functional Analysis Metric Geometry 49Q20 (Primary), 49J52, 53C23 (Secondary) |
| url | https://arxiv.org/abs/2412.04574 |