Alessio Figalli, Yi Ru-Ya Zhang
Published 2020-03-09Version 1
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 $p<2$, while it depends on $p$ for $p>2$.
Some remarks on the Sobolev inequality in Riemannian manifolds
Sharp Sobolev inequalities via projection averages
The sharp Poincaré--Sobolev type inequalities in the hyperbolic spaces $\mathbb H^n$
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