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Sharp regularity
estimates for solutions of the continuity equation drifted by
Sobolev vector fields
Elia Bruè and Quoc-Hung Nguyen |
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Vol. 14 (2021), No. 8, 2539–2559
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Abstract |
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The aim of this note is to prove sharp regularity estimates for solutions of the continuity equation, associated to vector fields for . The regularity is of “logarithmic order” and is measured by means of suitable seminorms. |
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Keywords
ordinary differential equations with nonsmooth vector
fields, continuity equation, transport equation, regular
Lagrangian flow, BV function, log-Sobolev space, Bressan's
mixing conjecture
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Mathematical Subject Classification 2010
Primary: 34A12, 35F10, 35F25
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Milestones
Received: 27 October 2019
Revised: 24 May 2020
Accepted: 31 July 2020
Published: 19 December 2021
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Authors |
| Elia Bruè | |
| Scuola Normale Superiore Pisa Italy |
School of Mathematics Institute for Advanced Study Princeton, NJ United States |
| Quoc-Hung Nguyen | |
| Scuola Normale Superiore Pisa Italy |
Academy of Mathematics and Systems
Science Chinese Academy of Sciences Beijing China |
