On the Gromov--Hausdorff stability of metric viscosity solutions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913933273595904 |
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| author | Makida, Shimpei |
| author_facet | Makida, Shimpei |
| contents | We establish the stability of metric viscosity solutions to first-order Hamilton--Jacobi equations under Gromov--Hausdorff convergence. Our proof combines a characterization of metric viscosity solutions via quadratic distance functions with a doubling variable method adapted to epsilon-isometries, which allows us to pass to the Gromov--Hausdorff limit without embedding the spaces into a common ambient space. As a byproduct, we give a PDE-based proof of the stability of the dual Kantorovich problems under measured-Gromov--Hausdorff convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Gromov--Hausdorff stability of metric viscosity solutions Makida, Shimpei Analysis of PDEs Metric Geometry 35D40, 35F21, 53C23 We establish the stability of metric viscosity solutions to first-order Hamilton--Jacobi equations under Gromov--Hausdorff convergence. Our proof combines a characterization of metric viscosity solutions via quadratic distance functions with a doubling variable method adapted to epsilon-isometries, which allows us to pass to the Gromov--Hausdorff limit without embedding the spaces into a common ambient space. As a byproduct, we give a PDE-based proof of the stability of the dual Kantorovich problems under measured-Gromov--Hausdorff convergence. |
| title | On the Gromov--Hausdorff stability of metric viscosity solutions |
| topic | Analysis of PDEs Metric Geometry 35D40, 35F21, 53C23 |
| url | https://arxiv.org/abs/2507.06495 |