KFU. Card publication. Estimates of generalized St. Venant functionals

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ESTIMATES OF GENERALIZED ST. VENANT FUNCTIONALS

Form of presentation

Articles in international journals and collections

Year of publication

2024

Язык

английский

Authors, employees of KFU

Avkhadiev Farit Gabidinovich, author

Bibliographic description in the original language

Avkhadiev F.G. Estimates of generalized St. Venant functionals/ // Lobachevskii J. Math. 2024, vol/ 45, No. 6, p. 2810--2820.

Annotation

In this paper we consider parametric generalizations of a St. Venant type functional, defined on domains of the Euclidean space of dimension $n\geq 2$ and connected with the torsional rigidity of a domain as well as with integrals of powers of the St. Venant stress function over simply connected plane domains. We give several estimates for the generalized functionals. In particular, for bounded convex domains we obtain an essential improvement of two known results proved by R.~Ba\~{n}uelos, M.~van~den~Berg, and T.~Carrol (see J. London Math. Soc., 66 (2), 499--512, 2002) and by R.~G.~Salahudinov (see Russian Math. (Iz. VUZ), 50:3, 39–46, 2006). In addition, we examine these functionals over non convex domains in two cases when a domain has uniformly perfect boundary or it is close to convex domains in a certain sense. For such a domain we prove several new estimates using power boundary moments of domains.

Keywords

St Venant a functional, torsional rigidity

The name of the journal

Lobashevskii Journal of Mathematics

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

https://repository.kpfu.ru/eng/?p_id=305149&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Avkhadiev Farit Gabidinovich	ru_RU
dc.date.accessioned	2024-01-01T00:00:00Z	ru_RU
dc.date.available	2024-01-01T00:00:00Z	ru_RU
dc.date.issued	2024	ru_RU
dc.identifier.citation	Avkhadiev F.G. Estimates of generalized St. Venant functionals/ // Lobachevskii J. Math. 2024, vol/ 45, No. 6, p. 2810--2820.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=305149&p_lang=2	ru_RU
dc.description.abstract	Lobashevskii Journal of Mathematics	ru_RU
dc.description.abstract	In this paper we consider parametric generalizations of a St. Venant type functional, defined on domains of the Euclidean space of dimension $n\geq 2$ and connected with the torsional rigidity of a domain as well as with integrals of powers of the St. Venant stress function over simply connected plane domains. We give several estimates for the generalized functionals. In particular, for bounded convex domains we obtain an essential improvement of two known results proved by R.~Ba\~{n}uelos, M.~van~den~Berg, and T.~Carrol (see J. London Math. Soc., 66 (2), 499--512, 2002) and by R.~G.~Salahudinov (see Russian Math. (Iz. VUZ), 50:3, 39–46, 2006). In addition, we examine these functionals over non convex domains in two cases when a domain has uniformly perfect boundary or it is close to convex domains in a certain sense. For such a domain we prove several new estimates using power boundary moments of domains.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	St Venant a functional	ru_RU
dc.subject	torsional rigidity	ru_RU
dc.title	Estimates of generalized St. Venant functionals	ru_RU
dc.type	Articles in international journals and collections	ru_RU