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Sbornik: Mathematics, 2018, Volume 209, Issue 3, Pages 292–319
DOI: https://doi.org/10.1070/SM8739 (Mi sm8739) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Rellich inequalities for polyharmonic operators in plane domains

F. G. Avkhadiev

Kazan (Volga Region) Federal University
English version PDF (609 kB) Citations (7)
References:
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DOI: https://doi.org/10.1070/SM8739
Abstract: Functionals whose values are defined as sharp constants in Rellich inequalities are investigated for polyharmonic operators in plane domains. The weight function is taken to be a power of the distance of a point to the boundary of the domain. Estimates are obtained for arbitrary domains, as is a test for these constants to be positive, and precise values are found for convex domains and for domains close to convex in a certain sense. The case when the weight function is taken to be a power of the coefficient in the Poincaré metric is also treated.
Bibliography: 28 titles.
Keywords: Rellich inequality, polyharmonic operator, uniformly perfect set, Poincaré metric.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00282-а
15-41-02433 р_поволжье
This research was carried out with the support of the Russian Foundation for Basic Research (grant nos. 17-01-00282-a and 15-41-02433 {\selectlanguage{russian}р_поволжье}).
Received: 19.05.2016 and 01.12.2016
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 3, Pages 4–33
DOI: https://doi.org/10.4213/sm8739
Bibliographic databases:
Document Type: Article
UDC: 517.54+517.518.28+517.956.2
MSC: 35A23
Language: English
Original paper language: Russian
Citation: F. G. Avkhadiev, “Rellich inequalities for polyharmonic operators in plane domains”, Mat. Sb., 209:3 (2018), 4–33; Sb. Math., 209:3 (2018), 292–319
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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