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

Abstract

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

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• A Lemma and a Conjecture on the Cost of Rearrangements

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