Russian Mathematics

, Volume 63, Issue 6, pp 74–78 | Cite as

On Extremal Domains for Integral Inequalities in the Euclidean Space

  • F. G. AvkhadievEmail author
Brief Communications


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.


Hardy inequality Rellich inequality 


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This work was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (1.9773.2017/8.9), and by the RFBR, grant no. 17-01-00282-a.


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Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Kazan Federal UniversityKazanRussia

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