КФУ. Карточка публикации. Estimates of generalized St. Venant functionals

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ESTIMATES OF GENERALIZED ST. VENANT FUNCTIONALS

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2024

Язык

английский

Авторы, сотрудники КФУ

Авхадиев Фарит Габидинович, автор

Библиографическое описание на языке оригинала

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

Аннотация

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.

Ключевые слова

St Venant a functional, torsional rigidity

Название журнала

Lobashevskii Journal of Mathematics

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https://repository.kpfu.ru/?p_id=305149

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Авхадиев Фарит Габидинович	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/?p_id=305149	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	Статьи в зарубежных журналах и сборниках	ru_RU