A note on the Gagliardo-Nirenberg inequality in a bounded domain

Congming Li; Kai Zhang

doi:10.3934/cpaa.2022132

Article Contents

2022, Volume 21, Issue 12: 4013-4017. Doi: 10.3934/cpaa.2022132

This issue Previous Article Asymptotic evaluations for multivariate Mellin convolution operators Next Article Spectral stability of small-amplitude dispersive shocks in quantum hydrodynamics with viscosity

A note on the Gagliardo-Nirenberg inequality in a bounded domain

Congming Li and
Kai Zhang^,

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China

^*Corresponding author: Kai Zhang
^*Corresponding author: Kai Zhang

Received: March 2022

Revised: March 2022

Early access: September 2022

Published online: September 2022

Both authors are supported by the National Natural Science Foundation of China (Grant No. 12031012 and 11831003) and the Institute of Modern Analysis-A Frontier Research Center of Shanghai. The second author is also supported by the China Postdoctoral Science Foundation (Grant No. 2022M712081).

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Abstract

The classical Gagliardo-Nirenberg inequality was established in $ \mathbb{R}^n $. An extension to a bounded domain was given by Gagliardo in 1959. In this note, we present a simple proof of this result and prove a new Gagliardo-Nirenberg inequality in a bounded Lipschitz domain.

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Mathematics Subject Classification: Primary: 26D10, 35A23, 46E35.

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References

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