Abstract
We prove a sharp quantitative version of the p-Sobolev inequality for any , with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for , while it depends on p for .
Citation
Alessio Figalli. Yi Ru-Ya Zhang. "Sharp gradient stability for the Sobolev inequality." Duke Math. J. 171 (12) 2407 - 2459, 1 September 2022. https://doi.org/10.1215/00127094-2022-0051
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