Differential and Integral Equations

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

Motohiro Sobajima

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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

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

First available in Project Euclid: 18 February 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


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.

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