## Differential and Integral Equations

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

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1455806023

**Mathematical Reviews number (MathSciNet)**

MR3466165

**Zentralblatt MATH identifier**

1374.26043

**Subjects**

Primary: 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47) 35Pxx: Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05]

#### Citation

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