## Differential and Integral Equations

### Remarks on higher-order weighted Rellich inequalities in $L^p$

Motohiro Sobajima

#### Abstract

The validity of higher-order weighted Rellich inequalities with respect to $L^p$-norm in $\mathbb R^N$ ($\||x|^{\alpha-2m}u\|_{L^p}\leq C\||x|^{\alpha}\Delta u\|_{L^p}$) for $N\in \mathbb N$, $1\leq p\leq \infty$, $m\in\mathbb N$ and $\alpha\in\mathbb R$ is investigated. The result generalizes the validity of weighted Rellich inequalities obtained in [6].

#### Article information

Source
Differential Integral Equations Volume 29, Number 3/4 (2016), 229-240.

Dates
First available in Project Euclid: 18 February 2016

Sobajima, Motohiro. Remarks on higher-order weighted Rellich inequalities in $L^p$. Differential Integral Equations 29 (2016), no. 3/4, 229--240.https://projecteuclid.org/euclid.die/1455806023