Propagation of regularity of level sets for a class of active transport equations

Abstract We prove that for any α ∈ ( 0 , 1 ) , the C 1 , α regularity of level sets for solutions to a class of active transport equations is propagated over the existence time of the solution. This extends a recent result of Bertozzi, Garnett, Laurent, and Verdera for patch boundary regularity for the aggregation equation.

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