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dc.contributor.author | Avkhadiev F. | |
dc.date.accessioned | 2018-09-19T20:15:57Z | |
dc.date.available | 2018-09-19T20:15:57Z | |
dc.date.issued | 2016 | |
dc.identifier.issn | 0022-247X | |
dc.identifier.uri | https://dspace.kpfu.ru/xmlui/handle/net/142767 | |
dc.description.abstract | © 2016 Elsevier Inc.For test functions supported in a domain of the Euclidean space we consider the Hardy-Rellich inequality: ∫|δf|2dx≥C2∫|f|2δ-4(x)dx, where C2=const≥0 and δ(x) is the distance from x to the boundary of the domain. M.P. Owen proved that this inequality is valid in any convex domain with C2=9/16 (M.P. Owen (1999) [21]). We examine the inequality in non-convex domains. It is proved that a positive constant C2 for a plane domain exists if and only if its boundary is a uniformly perfect set. For a domain of dimension d≥2 we prove that the inequality holds with the sharp constant C2=9/16, if the domain satisfies an exterior sphere condition with certain restriction on the radius of the sphere. In addition, we obtain similar results for the inequality ∫δ2(x)|δf|2dx≥C2*∫|f|2δ-2(x)dx. | |
dc.relation.ispartofseries | Journal of Mathematical Analysis and Applications | |
dc.subject | Hardy-Rellich inequality | |
dc.subject | Non-convex domain | |
dc.subject | Uniformly perfect set | |
dc.title | Hardy-Rellich inequalities in domains of the Euclidean space | |
dc.type | Article | |
dc.relation.ispartofseries-issue | 2 | |
dc.relation.ispartofseries-volume | 442 | |
dc.collection | Публикации сотрудников КФУ | |
dc.relation.startpage | 469 | |
dc.source.id | SCOPUS0022247X-2016-442-2-SID84965116506 |