Regularity of Lagrangian flows over RCD*(K, N) spaces
The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas already present in the literature, that flows generated by vecto...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
De Gruyter
2019
|
| _version_ | 1797093060066148352 |
|---|---|
| author | Brué, E Semola, D |
| author_facet | Brué, E Semola, D |
| author_sort | Brué, E |
| collection | OXFORD |
| description | The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas already present in the literature, that flows generated by vector fields with bounded symmetric derivative are Lipschitz, providing the natural extension of the standard Cauchy–Lipschitz theorem to this setting. Then we prove a Lusin-type regularity result in the Sobolev case (under the additional assumption that the m.m.s. is Ahlfors regular) therefore extending the already known Euclidean result. |
| first_indexed | 2024-03-07T03:54:53Z |
| format | Journal article |
| id | oxford-uuid:c288c3f3-8390-493a-918b-c8d11ccf144a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:54:53Z |
| publishDate | 2019 |
| publisher | De Gruyter |
| record_format | dspace |
| spelling | oxford-uuid:c288c3f3-8390-493a-918b-c8d11ccf144a2022-03-27T06:09:47ZRegularity of Lagrangian flows over RCD*(K, N) spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c288c3f3-8390-493a-918b-c8d11ccf144aEnglishSymplectic ElementsDe Gruyter2019Brué, ESemola, DThe aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas already present in the literature, that flows generated by vector fields with bounded symmetric derivative are Lipschitz, providing the natural extension of the standard Cauchy–Lipschitz theorem to this setting. Then we prove a Lusin-type regularity result in the Sobolev case (under the additional assumption that the m.m.s. is Ahlfors regular) therefore extending the already known Euclidean result. |
| spellingShingle | Brué, E Semola, D Regularity of Lagrangian flows over RCD*(K, N) spaces |
| title | Regularity of Lagrangian flows over RCD*(K, N) spaces |
| title_full | Regularity of Lagrangian flows over RCD*(K, N) spaces |
| title_fullStr | Regularity of Lagrangian flows over RCD*(K, N) spaces |
| title_full_unstemmed | Regularity of Lagrangian flows over RCD*(K, N) spaces |
| title_short | Regularity of Lagrangian flows over RCD*(K, N) spaces |
| title_sort | regularity of lagrangian flows over rcd k n spaces |
| work_keys_str_mv | AT bruee regularityoflagrangianflowsoverrcdknspaces AT semolad regularityoflagrangianflowsoverrcdknspaces |