| Форма представления | Статьи в российских журналах и сборниках |
| Год публикации | 2019 |
| Язык | английский |
|
Салахудинов Рустем Гумерович, автор
|
| Библиографическое описание на языке оригинала |
R. G. Salakhudinov, “Some properties of functionals on level sets”, Ufimsk. Mat. Zh., 11:2 (2019), 118–129; Ufa Math. J., 11:2 (2019), 114–124 DOI: 10.13108/2019-11-2-114, http://mi.mathnet.ru/ufa475 |
| Аннотация |
In the paper we consider special functionals on a planar domain G constructed by means of the distance to the boundary ∂G and a classical warping function. The functionals depending on the distance function are considered for simply-connected domains. We also study the functionals depending on the warping function for a finite-connected domain. We prove that the property of isoperimetric monotonicity with respect to a free
parameter gives rise to another monotonicity, namely, the monotonicity of the functionals considered as the functions of the sets defined on subsets of the domain. Some partial cases of the inequality were earlier obtained by Payne. We note that the inequalities were successfully applied for justifying new estimates for the torsional rigidity of simply-connected
and multiply-connected domains. In particular, we construct new functionals of domains monotone in both its variables. Moreover, we find sharp estimates of variation rate of the functions, that is, we obtain sharp estimates of their derivatives. |
| Ключевые слова |
distance to boundary, warping function, Payne type inequality, isoperimetric
inequality, isoperimetric monotonicity. |
| Название журнала |
Ufa Mathematical Journal
|
| URL |
http://mi.mathnet.ru/ufa475 |
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=215838 |
| Файлы ресурса | |
|
|
Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Салахудинов Рустем Гумерович |
ru_RU |
| dc.date.accessioned |
2019-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2019-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2019 |
ru_RU |
| dc.identifier.citation |
R. G. Salakhudinov, “Some properties of functionals on level sets”, Ufimsk. Mat. Zh., 11:2 (2019), 118–129; Ufa Math. J., 11:2 (2019), 114–124 DOI: 10.13108/2019-11-2-114, http://mi.mathnet.ru/ufa475 |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/?p_id=215838 |
ru_RU |
| dc.description.abstract |
Ufa Mathematical Journal |
ru_RU |
| dc.description.abstract |
In the paper we consider special functionals on a planar domain G constructed by means of the distance to the boundary ∂G and a classical warping function. The functionals depending on the distance function are considered for simply-connected domains. We also study the functionals depending on the warping function for a finite-connected domain. We prove that the property of isoperimetric monotonicity with respect to a free
parameter gives rise to another monotonicity, namely, the monotonicity of the functionals considered as the functions of the sets defined on subsets of the domain. Some partial cases of the inequality were earlier obtained by Payne. We note that the inequalities were successfully applied for justifying new estimates for the torsional rigidity of simply-connected
and multiply-connected domains. In particular, we construct new functionals of domains monotone in both its variables. Moreover, we find sharp estimates of variation rate of the functions, that is, we obtain sharp estimates of their derivatives. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
distance to boundary |
ru_RU |
| dc.subject |
warping function |
ru_RU |
| dc.subject |
Payne type inequality |
ru_RU |
| dc.subject |
isoperimetric
inequality |
ru_RU |
| dc.subject |
isoperimetric monotonicity. |
ru_RU |
| dc.title |
Some properties of functionals on level sets |
ru_RU |
| dc.type |
Статьи в российских журналах и сборниках |
ru_RU |
|
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