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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 8, Pages 83–87 (Mi ivm9390)  

Brief communications

On Rellich's inequalities in the Euclidean spaces

F. G. Avkhadiev

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: On domains of the Euclidean spaces we consider inequalities for test functions and their Laplacians. We describe a family of domains having vanishing Rellich constants. For the Euclidean space of dimension 4 we present a new version of the Rellich inequality. In addition we prove new one-dimensional Rellich-type integral inequalities for linear combinations of test functions and their derivatives of orders one and two.

Keywords: Laplace operator, Rellich inequality, uniformly perfect set, real spherical harmonics, Hardy inequality.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.9773.2017/8.9


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:8, 71–75

Bibliographic databases:

UDC: 517.956
Received: 05.03.2018

Citation: F. G. Avkhadiev, “On Rellich's inequalities in the Euclidean spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 8, 83–87; Russian Math. (Iz. VUZ), 62:8 (2018), 71–75

Citation in format AMSBIB
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\paper On Rellich's inequalities in the Euclidean spaces
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 8
\pages 83--87
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\vol 62
\issue 8
\pages 71--75
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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