Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures
We characterise equality cases in matrix H¨older’s inequality and develop a divergence formulation of optimal transport of vector measures. As an application, we reprove the representation formula for measures in the polar cone to monotone maps. We generalise the last result to a wide class of polar...
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2021
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| _version_ | 1797103307399888896 |
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| author | Ciosmak, KJ |
| author_facet | Ciosmak, KJ |
| author_sort | Ciosmak, KJ |
| collection | OXFORD |
| description | We characterise equality cases in matrix H¨older’s inequality and develop a divergence
formulation of optimal transport of vector measures. As an application, we reprove the representation
formula for measures in the polar cone to monotone maps. We generalise the last result to a wide class
of polar cones, including polar cones to tangent cones to the unit ball in the space of differentiable
functions and in the Sobolev spaces. |
| first_indexed | 2024-03-07T06:18:15Z |
| format | Journal article |
| id | oxford-uuid:f1d377f8-af01-4c80-8ebe-74327fda00fb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:18:15Z |
| publishDate | 2021 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:f1d377f8-af01-4c80-8ebe-74327fda00fb2022-03-27T11:59:00ZMatrix Hölder's inequality and divergence formulation of optimal transport of vector measuresJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f1d377f8-af01-4c80-8ebe-74327fda00fbEnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2021Ciosmak, KJWe characterise equality cases in matrix H¨older’s inequality and develop a divergence formulation of optimal transport of vector measures. As an application, we reprove the representation formula for measures in the polar cone to monotone maps. We generalise the last result to a wide class of polar cones, including polar cones to tangent cones to the unit ball in the space of differentiable functions and in the Sobolev spaces. |
| spellingShingle | Ciosmak, KJ Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures |
| title | Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures |
| title_full | Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures |
| title_fullStr | Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures |
| title_full_unstemmed | Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures |
| title_short | Matrix Hölder's inequality and divergence formulation of optimal transport of vector measures |
| title_sort | matrix holder s inequality and divergence formulation of optimal transport of vector measures |
| work_keys_str_mv | AT ciosmakkj matrixholdersinequalityanddivergenceformulationofoptimaltransportofvectormeasures |