KFU. Card publication. Hardy-Rellich inequalities in domains of the Euclidean space

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FEDERAL UNIVERSITY

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HARDY-RELLICH INEQUALITIES IN DOMAINS OF THE EUCLIDEAN SPACE

Form of presentation

Articles in international journals and collections

Year of publication

2016

Язык

английский

Authors, employees of KFU

Avkhadiev Farit Gabidinovich, author

Bibliographic description in the original language

Avkhadiev F.G. Hardy-Rellich inequalities in domains of the Euclidean space. J. Math. Anal. Appl., 442(2016), 469-484.

Annotation

For test functiond supported in a domain of the Euclidean space we consider the Hardy-Rellich inequality when the weight is a power of the distance to the boundary of the domain. We examine the Owen result foe convex domain in the case of non-convex domain/ It is proved that a positive constant for a plane domain exists if and only if the boundary of the domain is a uniformly perfect set. Also, we obtain several sharp estimates of constants for multidimensional non-convex domains.

Keywords

Hardy-Rellich inequality, non-convex domain, uniformly perfect set

The name of the journal

J MATH ANAL APPL

URL

http://www.elsevier.com/locate/jmaa

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=131919&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Avkhadiev Farit Gabidinovich	ru_RU
dc.date.accessioned	2016-01-01T00:00:00Z	ru_RU
dc.date.available	2016-01-01T00:00:00Z	ru_RU
dc.date.issued	2016	ru_RU
dc.identifier.citation	Avkhadiev F.G. Hardy-Rellich inequalities in domains of the Euclidean space. J. Math. Anal. Appl., 442(2016), 469-484.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=131919&p_lang=2	ru_RU
dc.description.abstract	J MATH ANAL APPL	ru_RU
dc.description.abstract	For test functiond supported in a domain of the Euclidean space we consider the Hardy-Rellich inequality when the weight is a power of the distance to the boundary of the domain. We examine the Owen result foe convex domain in the case of non-convex domain/ It is proved that a positive constant for a plane domain exists if and only if the boundary of the domain is a uniformly perfect set. Also, we obtain several sharp estimates of constants for multidimensional non-convex domains.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hardy-Rellich inequality	ru_RU
dc.subject	non-convex domain	ru_RU
dc.subject	uniformly perfect set	ru_RU
dc.title	Hardy-Rellich inequalities in domains of the Euclidean space	ru_RU
dc.type	Articles in international journals and collections	ru_RU