dc.contributor.author |
Salakhudinov R. |
|
dc.date.accessioned |
2018-09-18T20:31:34Z |
|
dc.date.available |
2018-09-18T20:31:34Z |
|
dc.date.issued |
2012 |
|
dc.identifier.issn |
0036-1410 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/140784 |
|
dc.description.abstract |
Euclidean moments of simply connected plane domains are investigated. The moments are defined as the pth power of the L p-norms of the distance function to the boundary of the domain. As was shown by Avkhadiev (1998) the Euclidean moment of inertia (p = 2) gives two-sided estimates for the torsional rigidity of the domain. The estimate of the torsional rigidity connected with the domain area is the famous Saint-Venant-Pólya inequality, which was refined by Payne (1962). In this paper we obtain Payne-type inequalities for the Euclidean moments. A surprising fact is that new extremal domains, different from a disk, are found. © 2012 Society for Industrial and Applied Mathematics. |
|
dc.relation.ispartofseries |
SIAM Journal on Mathematical Analysis |
|
dc.subject |
Bonnesen's inequality |
|
dc.subject |
Euclidean moments of a domain with respect to its boundary |
|
dc.subject |
Isoperimetric inequality |
|
dc.subject |
Torsional rigidity |
|
dc.title |
Refined inequalities for Euclidean moments of a domain with respect to its boundary |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
4 |
|
dc.relation.ispartofseries-volume |
44 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
2949 |
|
dc.source.id |
SCOPUS00361410-2012-44-4-SID84866068231 |
|