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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 8, Pages 83–87 (Mi ivm9390)  
This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

On Rellich's inequalities in the Euclidean spaces

F. G. Avkhadiev

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
Full-text PDF (179 kB) Citations (3)
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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
Received: 05.03.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, Volume 62, Issue 8, Pages 71–75
DOI: https://doi.org/10.3103/S1066369X18080108
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
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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\by F.~G.~Avkhadiev
\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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\jour Russian Math. (Iz. VUZ)
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\vol 62
\issue 8
\pages 71--75
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Linking options:
  • https://www.mathnet.ru/eng/ivm9390
  • https://www.mathnet.ru/eng/ivm/y2018/i8/p83
    • This publication is cited in the following 3 articles:
    1. F. G. Avkhadiev, I. R. Kayumov, S. R. Nasyrov, “Extremal problems in geometric function theory”, Russian Math. Surveys, 78:2 (2023), 211–271  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. F. Avkhadiev, “Selected results and open problems on Hardy-Rellich and Poincare-Friedrichs inequalities”, Anal. Math. Phys., 11:3 (2021), 134  crossref  mathscinet  isi
    3. F. G. Avkhadiev, “On extremal domains for integral inequalities in the Euclidean space”, Russian Math. (Iz. VUZ), 63:6 (2019), 74–78  mathnet  crossref  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:47
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