A duality-based approach to gradient flows of linear growth functionals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910879258247168 |
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| author | Górny, Wojciech Mazón, José M. |
| author_facet | Górny, Wojciech Mazón, José M. |
| contents | We study gradient flows of general functionals with linear growth with very weak assumptions. Classical results concerning characterisation of solutions require differentiability of the Lagrangian, as for the time-dependent minimal surface equation, or a special form of the Lagrangian as in the total variation flow. We propose to study this problem using duality techniques, give a general definition of solutions and prove their existence and uniqueness. This approach also allows us to reduce the regularity and structure assumptions on the Lagrangian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08725 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A duality-based approach to gradient flows of linear growth functionals Górny, Wojciech Mazón, José M. Analysis of PDEs 35K65, 35K67, 35K92, 49N15 We study gradient flows of general functionals with linear growth with very weak assumptions. Classical results concerning characterisation of solutions require differentiability of the Lagrangian, as for the time-dependent minimal surface equation, or a special form of the Lagrangian as in the total variation flow. We propose to study this problem using duality techniques, give a general definition of solutions and prove their existence and uniqueness. This approach also allows us to reduce the regularity and structure assumptions on the Lagrangian. |
| title | A duality-based approach to gradient flows of linear growth functionals |
| topic | Analysis of PDEs 35K65, 35K67, 35K92, 49N15 |
| url | https://arxiv.org/abs/2212.08725 |