Absence of loops for the Wasserstein-$\mathcal{H}^1$ problem: the concentration/blow-up argument
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913043475070976 |
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| author | Machado, Jo{ã}o Miguel |
| author_facet | Machado, Jo{ã}o Miguel |
| contents | In the present work we prove that minimizers of the Wasserstein-$\mathscr{H}^1$ problem, introduced recently by Chambolle et. al., are trees in two cases: when the target measure is a sum of finitely many Dirac masses or when it has a bounded density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absence of loops for the Wasserstein-$\mathcal{H}^1$ problem: the concentration/blow-up argument Machado, Jo{ã}o Miguel Analysis of PDEs Optimization and Control In the present work we prove that minimizers of the Wasserstein-$\mathscr{H}^1$ problem, introduced recently by Chambolle et. al., are trees in two cases: when the target measure is a sum of finitely many Dirac masses or when it has a bounded density. |
| title | Absence of loops for the Wasserstein-$\mathcal{H}^1$ problem: the concentration/blow-up argument |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2505.09232 |