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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 |