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arXiv · 2310.03871

A note on a $L^p$ stability estimate for regular Lagrangian flows

Tommaso Cortopassi
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Abstract

In this note, we prove a $L^p$ version of the well known stability estimate for regular Lagrangian flows derived by Gianluca Crippa and Camillo De Lellis in \cite{crippa2008estimates}. As far as we know, the only estimate of this kind readily available in the literature is for the case $p=1$. With minor modifications to the proof in \cite{crippa2008estimates}, we show that an analogous estimate holds in $L^p$ norm with $p \in (1, + \infty)$.

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Tommaso Cortopassi. 2023-10-05. A note on a $L^p$ stability estimate for regular Lagrangian flows. https://arxiv.org/abs/2310.03871

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