Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields
Elia Brué, Quoc‐Hung Nguyen
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.
Topics & Concepts
LogarithmVector fieldSobolev spaceMathematicsClass (philosophy)Mathematical analysisOrder (exchange)Pure mathematicsApplied mathematicsComputer scienceGeometryEconomicsArtificial intelligenceFinanceAdvanced Harmonic Analysis ResearchNonlinear Partial Differential EquationsAdvanced Mathematical Physics Problems