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Remarks on a nonlocal transport
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Li, Dong and Rodrigo, Jose L. (2020) Remarks on a nonlocal transport. Advances in Mathematics, 374 (18). 107345. doi:10.1016/j.aim.2020.107345 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2020.107345
Abstract
We consider a one dimensional nonlocal transport equation and its natural multi-dimensional analogues. By using a new pointwise inequality for the Hilbert transform, we give a short proof of a nonlinear inequality first proved by Córdoba, Córdoba and Fontelos in 2005. We also prove several new weighted inequalities for the Hilbert transform and various nonlinear versions. Some of these results generalize to a related family of nonlocal models.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Hilbert transform , Differential equations, Partial | ||||||||||||
| Journal or Publication Title: | Advances in Mathematics | ||||||||||||
| Publisher: | Academic Press | ||||||||||||
| ISSN: | 0001-8708 | ||||||||||||
| Official Date: | 18 November 2020 | ||||||||||||
| Dates: |
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| Volume: | 374 | ||||||||||||
| Number: | 18 | ||||||||||||
| Article Number: | 107345 | ||||||||||||
| DOI: | 10.1016/j.aim.2020.107345 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Date of first compliant deposit: | 7 August 2020 | ||||||||||||
| Date of first compliant Open Access: | 5 August 2021 | ||||||||||||
| RIOXX Funder/Project Grant: |
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