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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.22093 |
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| _version_ | 1866912453660508160 |
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| author | Bormann, Marie Monsaingeon, Léonard Renger, D. R. Michiel von Renesse, Max |
| author_facet | Bormann, Marie Monsaingeon, Léonard Renger, D. R. Michiel von Renesse, Max |
| contents | We establish a representation of the heat flow with Wentzell boundary conditions on smooth domains as gradient descent dynamics for the entropy in a suitably extended Otto manifold of probability measures with additional boundary parts. Yet it is shown that for weak boundary diffusion, the associated Fokker-Planck dynamics cannot be recovered from any entropy-driven metric JKO-Wasserstein scheme, at least if the underlying point metric satisfies certain natural regularity assumptions. This discrepancy is illustrated in competing large-deviation heuristics in the Sanov and Schilder regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22093 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A gradient flow that is none: Heat flow with Wentzell boundary condition Bormann, Marie Monsaingeon, Léonard Renger, D. R. Michiel von Renesse, Max Analysis of PDEs Probability We establish a representation of the heat flow with Wentzell boundary conditions on smooth domains as gradient descent dynamics for the entropy in a suitably extended Otto manifold of probability measures with additional boundary parts. Yet it is shown that for weak boundary diffusion, the associated Fokker-Planck dynamics cannot be recovered from any entropy-driven metric JKO-Wasserstein scheme, at least if the underlying point metric satisfies certain natural regularity assumptions. This discrepancy is illustrated in competing large-deviation heuristics in the Sanov and Schilder regimes. |
| title | A gradient flow that is none: Heat flow with Wentzell boundary condition |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2506.22093 |