Published Paper
Inserted: 5 aug 2021
Last Updated: 10 feb 2023
Journal: Duke Mathematical Journal
Year: 2022
Abstract:
We prove a sharp quantitative version of the $p$-Sobolev inequality for any $1<p<n$, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p \leq 2$, while it depends on $p$ for $p>2$.
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