Abstract
AbstractTwo notions of “having a derivative of logarithmic order” have been studied. They come from the study of regularity of flows and renormalized solutions for the transport and continuity equation associated to weakly differentiable drifts.
Highlights
Two notions of “having a derivative of logarithmic order” have been studied. They come from the study of regularity of ows and renormalized solutions for the transport and continuity equation associated to weakly di erentiable drifts
In this note we study two di erent notions of "having derivative of logarithmic order"
In this setting the (ODE) problem has been studied, for a rst time, by DiPerna and Lions [1] and extended to the BV framework by Ambrosio in [2]. After these two pioneering works this topic has received a lot of attentions becoming a very thriving research eld
Summary
In this note we study two di erent notions of "having derivative of logarithmic order" They come up naturally in the study of regular Lagrangian ows and renormalized solutions for transport and continuity equation under the Sobolev regularity of the drift [1,2,3,4,5]. In this setting the (ODE) problem has been studied, for a rst time, by DiPerna and Lions [1] and extended to the BV framework by Ambrosio in [2]. After these two pioneering works this topic has received a lot of attentions becoming a very thriving research eld.
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