Regularity of optimal mapping between hypercubes
In this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri. The C3,α{C}^{3,\alpha } regularity is also optimal due to a counterexample i...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-09-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2023-0087 |
| _version_ | 1797653382047989760 |
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| author | Chen Shibing Liu Jiakun Wang Xu-Jia |
| author_facet | Chen Shibing Liu Jiakun Wang Xu-Jia |
| author_sort | Chen Shibing |
| collection | DOAJ |
| description | In this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri. The C3,α{C}^{3,\alpha } regularity is also optimal due to a counterexample in the study by Jhaveri. |
| first_indexed | 2024-03-11T16:43:51Z |
| format | Article |
| id | doaj.art-f51ed278e7834ae1b5350933cd2acf35 |
| institution | Directory Open Access Journal |
| issn | 2169-0375 |
| language | English |
| last_indexed | 2024-03-11T16:43:51Z |
| publishDate | 2023-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-f51ed278e7834ae1b5350933cd2acf352023-10-23T07:49:51ZengDe GruyterAdvanced Nonlinear Studies2169-03752023-09-0123137541710.1515/ans-2023-0087Regularity of optimal mapping between hypercubesChen Shibing0Liu Jiakun1Wang Xu-Jia2School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P.R. ChinaSchool of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, AustraliaCentre for Mathematics and Its Applications, The Australian National University, Canberra, ACT 0200, AustraliaIn this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri. The C3,α{C}^{3,\alpha } regularity is also optimal due to a counterexample in the study by Jhaveri.https://doi.org/10.1515/ans-2023-0087monge-ampère equationoptimal transportationglobal regularity35j9635j2535b65 |
| spellingShingle | Chen Shibing Liu Jiakun Wang Xu-Jia Regularity of optimal mapping between hypercubes Advanced Nonlinear Studies monge-ampère equation optimal transportation global regularity 35j96 35j25 35b65 |
| title | Regularity of optimal mapping between hypercubes |
| title_full | Regularity of optimal mapping between hypercubes |
| title_fullStr | Regularity of optimal mapping between hypercubes |
| title_full_unstemmed | Regularity of optimal mapping between hypercubes |
| title_short | Regularity of optimal mapping between hypercubes |
| title_sort | regularity of optimal mapping between hypercubes |
| topic | monge-ampère equation optimal transportation global regularity 35j96 35j25 35b65 |
| url | https://doi.org/10.1515/ans-2023-0087 |
| work_keys_str_mv | AT chenshibing regularityofoptimalmappingbetweenhypercubes AT liujiakun regularityofoptimalmappingbetweenhypercubes AT wangxujia regularityofoptimalmappingbetweenhypercubes |