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

Elia Bru\`e; Quoc-Hung Nguyen

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

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arxiv 1806.03466 v2 pith:QLPJSVYW submitted 2018-06-09 math.AP

Elia Bruè , Quoc-Hung Nguyen This is my paper · ORCID

classification math.AP

keywords regularitycontinuityequationestimatesfieldssharpsolutionsvector

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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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