Metric viscosity solutions and distance-like functions on the Wasserstein space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912173617315840 |
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| author | Jiang, Huajian Cui, Xiaojun |
| author_facet | Jiang, Huajian Cui, Xiaojun |
| contents | Viscosity solutions to the eikonal equation |Du|g = 1, known to be exactly distance-like functions, on a non-compact complete Riemannian manifold (M,g) are crucial for understanding the underlying geometric and topological properties. In this work, we explore metric viscosity solutions, distance-like functions and their relationship on a metric space, especially on the Wasserstein space Pp(X) where X is a complete, separable, locally compact and non-compact geodesic space. Meanwhile, we provide two distinct ways to construct (strong) metric viscosity solutions on Pp(X) and study their properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10618 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Metric viscosity solutions and distance-like functions on the Wasserstein space Jiang, Huajian Cui, Xiaojun Analysis of PDEs Viscosity solutions to the eikonal equation |Du|g = 1, known to be exactly distance-like functions, on a non-compact complete Riemannian manifold (M,g) are crucial for understanding the underlying geometric and topological properties. In this work, we explore metric viscosity solutions, distance-like functions and their relationship on a metric space, especially on the Wasserstein space Pp(X) where X is a complete, separable, locally compact and non-compact geodesic space. Meanwhile, we provide two distinct ways to construct (strong) metric viscosity solutions on Pp(X) and study their properties. |
| title | Metric viscosity solutions and distance-like functions on the Wasserstein space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.10618 |