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 |
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dc.subject |
Non-convex domain |
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dc.subject |
Uniformly perfect set |
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dc.title |
Hardy-Rellich inequalities in domains of the Euclidean space |
|
dc.type |
Article |
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dc.relation.ispartofseries-issue |
2 |
|
dc.relation.ispartofseries-volume |
442 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
469 |
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dc.source.id |
SCOPUS0022247X-2016-442-2-SID84965116506 |
|