Solutions to Monge-Ampère Equations with Low Codimensional singularities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913144150949888 |
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| author | Rakshit, Arghya Sen, Aranya |
| author_facet | Rakshit, Arghya Sen, Aranya |
| contents | We construct solutions to Monge-Ampère equations whose Monge-Ampère measures contain singular components supported on low codimensional sets. We also study the regularity of such solutions. To motivate our construction, we present examples arising from optimal transport where the potential of optimal transport maps satisfy Monge-Ampère equations similar to the ones we study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19142 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solutions to Monge-Ampère Equations with Low Codimensional singularities Rakshit, Arghya Sen, Aranya Analysis of PDEs 35J96, 49Q22 We construct solutions to Monge-Ampère equations whose Monge-Ampère measures contain singular components supported on low codimensional sets. We also study the regularity of such solutions. To motivate our construction, we present examples arising from optimal transport where the potential of optimal transport maps satisfy Monge-Ampère equations similar to the ones we study. |
| title | Solutions to Monge-Ampère Equations with Low Codimensional singularities |
| topic | Analysis of PDEs 35J96, 49Q22 |
| url | https://arxiv.org/abs/2605.19142 |