Geodesic
On extremal domains for integral inequalities in the Euclidean space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2019), pp. 80-84

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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. 
@article{IVM_2019_6_a7,
     author = {F. G. Avkhadiev},
     title = {On extremal domains for integral inequalities in the {Euclidean} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {80--84},
     publisher = {mathdoc},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_6_a7/}
}
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F. G. Avkhadiev. On extremal domains for integral inequalities in the Euclidean space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2019), pp. 80-84. http://geodesic.mathdoc.fr/item/IVM_2019_6_a7/