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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 6, Pages 1205–1217
DOI: https://doi.org/10.17377/smzh.2017.58.602 (Mi smj2931) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The generalized Davies problem for polyharmonic operators

F. G. Avkhadiev

Kazan (Volga Region) Federal University, Kazan, Russia
Full-text PDF (325 kB) Citations (4)
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DOI: https://doi.org/10.17377/smzh.2017.58.602
Abstract: The Davies problem is connected with the maximal constants in Hardy-type inequalities. We study the generalizations of this problem to the Rellich-type inequalities for polyharmonic operators in domains of the Euclidean space. The estimates are obtained solving the generalized problem under an additional minimal condition on the boundary of the domain. Namely, for a given domain we assume the existence of two balls with sufficiently small radii and the following property: the balls have only a sole common point; one ball lies inside the domain and the other is disjoint from the domain.
Keywords: polyharmonic operator, Rellich-type inequality, distance.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00282-a
The author was supported by the Russian Foundation for Basic Research (Grant 17-01-00282-a).
Received: 21.04.2017
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 6, Pages 932–942
DOI: https://doi.org/10.1134/S0037446617060027
Bibliographic databases:
Document Type: Article
UDC: 517.5+517.956.225
MSC: 35R30
Language: Russian
Citation: F. G. Avkhadiev, “The generalized Davies problem for polyharmonic operators”, Sibirsk. Mat. Zh., 58:6 (2017), 1205–1217; Siberian Math. J., 58:6 (2017), 932–942
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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