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arXiv · 2510.24022

Stability estimates for $L^p$-Caffarelli-Kohn-Nirenberg inequalities

Xiao-Ping Chen·Chun-Lei Tang
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Abstract

Based on some new vector inequalities established by Figalli and Zhang [\emph{Duke Math. J.} \textbf{171} (2022), 2407--2459], we study the stability of the scale invariant and the scale non-invariant $L^p$-Caffarelli-Kohn-Nirenberg inequalities, which fills the recent work of Do \emph{et al.} [$L^p$-Caffarelli-Kohn-Nirenberg inequalities and their stabilities, arXiv: 2310.07083] for $1<p<2$, and also extends some results of Cazacu \emph{et al.} [\emph{J. Math. Pures Appl. (9)} \textbf{182} (2024), 253--284] to a general case for $L^p$-Caffarelli-Kohn-Nirenberg inequalities with $1<p<N$.

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Xiao-Ping Chen, Chun-Lei Tang. 2025-10-28. Stability estimates for $L^p$-Caffarelli-Kohn-Nirenberg inequalities. https://arxiv.org/abs/2510.24022

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