A few topics on total variation flows
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914659624288256 |
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| author | Giga, Yoshikazu Kuroda, Hirotoshi Łasica, Michał |
| author_facet | Giga, Yoshikazu Kuroda, Hirotoshi Łasica, Michał |
| contents | Total variation gradient flows are important in several applied fields, including image analysis and materials science. In this paper, we review a few basic topics including definition of a solution, explicit examples and the notion of calibrability, finite time extinction, and some regularity properties of solutions. We focus on the second-order flow (possibly with weights) and the fourth-order flow. We also discuss the fractional cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A few topics on total variation flows Giga, Yoshikazu Kuroda, Hirotoshi Łasica, Michał Analysis of PDEs Total variation gradient flows are important in several applied fields, including image analysis and materials science. In this paper, we review a few basic topics including definition of a solution, explicit examples and the notion of calibrability, finite time extinction, and some regularity properties of solutions. We focus on the second-order flow (possibly with weights) and the fourth-order flow. We also discuss the fractional cases. |
| title | A few topics on total variation flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.17179 |