First variation of functional Wulff shapes
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909210717978624 |
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| author | Ulivelli, Jacopo |
| author_facet | Ulivelli, Jacopo |
| contents | We introduce functional Wulff shapes based on the classical construction for compact convex sets. With this new tool, we establish a functional version of Aleksandrov's variational lemma in the family of convex functions with compact domain. The resulting formula is then applied to evaluate the first variation of a class of functionals on convex functions. In particular, we extend a recent result by Huang, Liu, Xi, and Zhao. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11172 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | First variation of functional Wulff shapes Ulivelli, Jacopo Metric Geometry Functional Analysis 52A20, 52A38, 49J53 We introduce functional Wulff shapes based on the classical construction for compact convex sets. With this new tool, we establish a functional version of Aleksandrov's variational lemma in the family of convex functions with compact domain. The resulting formula is then applied to evaluate the first variation of a class of functionals on convex functions. In particular, we extend a recent result by Huang, Liu, Xi, and Zhao. |
| title | First variation of functional Wulff shapes |
| topic | Metric Geometry Functional Analysis 52A20, 52A38, 49J53 |
| url | https://arxiv.org/abs/2312.11172 |