Calculus of Variations and Geometric Measure Theory
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E. Bruè - Q. H. Nguyen

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

created by bruè on 09 Jun 2018
modified on 17 Nov 2020

[BibTeX]

Accepted Paper

Inserted: 9 jun 2018
Last Updated: 17 nov 2020

Journal: Analysis and PDE
Pages: 18
Year: 2018

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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