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

2021/10/25 by Congming Li, Kai Zhang, Li, Congming +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2110.12967

Abstract

The classical Gagliardo-Nirenberg inequality was established in ℝⁿ. 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.

Cited by

• Finite time blow-up analysis for the generalized Proudman-Johnson model
• Quasi-optimal error estimates for the approximation of stable stationary states of the elastic energy of inextensible curves

Related

• Gagliardo-Nirenberg-Sobolev inequalities for convex domains in ℝ^d
• A Stability Result for a Family of Sharp Gagliardo-Nirenberg Inequalities
• On Gagliardo-Nirenberg type inequalities
• A Gagliardo-Nirenberg type inequality for rapidly decaying functions
• Gagliardo-Nirenberg inequality with Hölder norms