Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields

Elia Bruè; Quoc-Hung Nguyen

doi:10.2140/apde.2021.14.2539

Abstract

The aim of this note is to prove sharp regularity estimates for solutions of the continuity equation, associated to ${W^{1,p}}$ vector fields for $p > 1$ . The regularity is of “logarithmic order” and is measured by means of suitable seminorms.

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Elia Bruè. Quoc-Hung Nguyen. "Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields." Anal. PDE 14 (8) 2539 - 2559, 2021. https://doi.org/10.2140/apde.2021.14.2539

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Received: 27 October 2019; Revised: 24 May 2020; Accepted: 31 July 2020; Published: 2021

First available in Project Euclid: 17 February 2022

MathSciNet: MR4377866

zbMATH: 1485.35091

Digital Object Identifier: 10.2140/apde.2021.14.2539

Subjects:

Primary: 34A12 , 35F10 , 35F25

Keywords: Bressan’s mixing conjecture , BV function , continuity equation , log-Sobolev space , ordinary differential equations with nonsmooth vector fields , regular Lagrangian flow , transport equation

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