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On Rellich’s Inequalities in Euclidean Spaces

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Abstract

On domains of 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.

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Authors and Affiliations

  1. Kazan Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    F. G. Avkhadiev

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  1. F. G. Avkhadiev
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Correspondence to F. G. Avkhadiev.

Additional information

Original Russian Text © F.G. Avkhadiev, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 8, pp. 83–87.

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Avkhadiev, F.G. On Rellich’s Inequalities in Euclidean Spaces. Russ Math. 62, 71–75 (2018). https://doi.org/10.3103/S1066369X18080108

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  • DOI: https://doi.org/10.3103/S1066369X18080108

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