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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 6, Pages 80–84
DOI: https://doi.org/10.26907/0021-3446-2019-6-80-84 (Mi ivm9475) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

On extremal domains for integral inequalities in the Euclidean space

F. G. Avkhadiev

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2019-6-80-84
Abstract: On domains of the Euclidean space we consider Hardy and Rellich type inequalities with weight functions depending on the distance to the boundary of the domain. We show that extremal domains are not single for some known inequalities with sharp estimates of constants. We describe a family of extremal domains for Hardy type inequalities of a general form. On plane domains we study a new Rellich type inequality having a similar property.
Keywords: Hardy inequality, Rellich inequality.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.9773.2017/8.9
Russian Foundation for Basic Research 17-01-00282_a
Received: 24.02.2019
Revised: 24.02.2019
Accepted: 27.03.2019
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 6, Pages 74–78
DOI: https://doi.org/10.3103/S1066369X19060082
Bibliographic databases:
Document Type: Article
UDC: 517.5: 517.956
Language: Russian
Citation: F. G. Avkhadiev, “On extremal domains for integral inequalities in the Euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 6, 80–84; Russian Math. (Iz. VUZ), 63:6 (2019), 74–78
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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