On a sharp Gagliardo–Nirenberg-type inequality

Yong Chen; Yi C. Huang

doi:10.4171/pm/2166

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On a sharp Gagliardo–Nirenberg-type inequality

Yong Chen
Baoshan University, P. R. China
Yi C. Huang
Nanjing Normal University, P. R. China

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Abstract

We provide a complete proof of a sharp Gagliardo–Nirenberg-type inequality on the unit interval, in its additive-invariant form

c \in R in f ∥ f - c ∥_{L^{\infty}} \leq (\frac{3}{2})^{1/3} (c \in R in f ∥ f - c ∥_{L^{2}})^{2/3} ∥ f^{'} ∥_{L^{\infty}}^{1/3},

which is motivated by the quantitative stability analysis in optimal transport theory. The proof employs the one-dimensional area formula together with rather elementary calculations.

Cite this article

Yong Chen, Yi C. Huang, On a sharp Gagliardo–Nirenberg-type inequality. Port. Math. (2026), published online first

DOI 10.4171/PM/2166