A model of anisotropic branched optimal transport
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915943739817984 |
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| author | Bellettini, Martina Marchese, Andrea |
| author_facet | Bellettini, Martina Marchese, Andrea |
| contents | We propose a new anisotropic optimal transport model based on the theory of currents, where the anisotropic cost function splits as the product of a factor depending only on the spatial direction and a factor depending only on the multiplicity of the current. We prove that the planar transport problem admits a minimizer. In arbitrary dimension, we show that a minimizer exists provided that the ambient space endowed with the anisotropic norm is hypermetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17123 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A model of anisotropic branched optimal transport Bellettini, Martina Marchese, Andrea Optimization and Control Analysis of PDEs We propose a new anisotropic optimal transport model based on the theory of currents, where the anisotropic cost function splits as the product of a factor depending only on the spatial direction and a factor depending only on the multiplicity of the current. We prove that the planar transport problem admits a minimizer. In arbitrary dimension, we show that a minimizer exists provided that the ambient space endowed with the anisotropic norm is hypermetric. |
| title | A model of anisotropic branched optimal transport |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2604.17123 |