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Lower bound for the hardy constant for an arbitrary domain in R<sup>n</sup>

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dc.contributor.author Shafigullin I.
dc.date.accessioned 2018-04-05T07:10:25Z
dc.date.available 2018-04-05T07:10:25Z
dc.date.issued 2017
dc.identifier.uri http://dspace.kpfu.ru/xmlui/handle/net/130440
dc.description.abstract © I.K. Shafigullin. 2017. In the paper we consider the conjecture by E.B. Davies on an uniform lower bound for the Hardy constant. We provide the known counterexamples rebutting this conjecture for the dimension 4 and higher. In the work we obtain non-zero lower bounds for the Hardy constants. These estimates are order sharp as n → +∞, where n is the space dimension. Moreover, these estimates are independent of the properties of the considered domains and are true for all domains not coinciding with the entire space. In the proof of the main theorem we reduce the multidimensional case to the one-dimensional case by choosing special classes of functions. As a result, the considered inequalities are reduced to the well-known Poincaré inequality.
dc.subject Hardy constant
dc.subject Hardy inequalities
dc.subject Lower bounds
dc.subject Variational inequalities
dc.title Lower bound for the hardy constant for an arbitrary domain in R<sup>n</sup>
dc.type Article
dc.relation.ispartofseries-issue 2
dc.relation.ispartofseries-volume 9
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 102
dc.source.id SCOPUS-2017-9-2-SID85023633332


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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