Residual sets of functions, wave speeds, and velocity fields exhibit pathological behaviors that previous results only constructed as single counterexamples.
Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields
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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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math.FA 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Residual pathologies
Residual sets of functions, wave speeds, and velocity fields exhibit pathological behaviors that previous results only constructed as single counterexamples.