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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.15007 |
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| _version_ | 1866911010855583744 |
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| author | Carioni, Marcello Krautz, Juliane Pietschmann, Jan-F. |
| author_facet | Carioni, Marcello Krautz, Juliane Pietschmann, Jan-F. |
| contents | We study an optimal transport problem in a compact convex set $Ω\subset\mathbb{R}^d$ where bulk transport is coupled to dynamic optimal transport on a metric graph $ \mathsf{G} = (\mathsf{V},\mathsf{E})$ which is embedded in $Ω$. We prove existence of solutions for fixed graphs. Next, we consider varying graphs, yet only for the case of star-shaped ones. Here, the action functional is augmented by an additional penalty that prevents the edges of the graph to overlap. This allows to preserve the graph topology and thus to rely on standard techniques in Calculus of Variations in order to show existence of minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamic Optimal Transport with optimal star shaped graphs Carioni, Marcello Krautz, Juliane Pietschmann, Jan-F. Analysis of PDEs We study an optimal transport problem in a compact convex set $Ω\subset\mathbb{R}^d$ where bulk transport is coupled to dynamic optimal transport on a metric graph $ \mathsf{G} = (\mathsf{V},\mathsf{E})$ which is embedded in $Ω$. We prove existence of solutions for fixed graphs. Next, we consider varying graphs, yet only for the case of star-shaped ones. Here, the action functional is augmented by an additional penalty that prevents the edges of the graph to overlap. This allows to preserve the graph topology and thus to rely on standard techniques in Calculus of Variations in order to show existence of minimizers. |
| title | Dynamic Optimal Transport with optimal star shaped graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.15007 |