KFU. Card publication. Some properties of functionals on level sets

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FEDERAL UNIVERSITY

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SOME PROPERTIES OF FUNCTIONALS ON LEVEL SETS

Form of presentation

Articles in Russian journals and collections

Year of publication

2019

Язык

английский

Authors, employees of KFU

Salakhudinov Rustem Gumerovich, author

Bibliographic description in the original language

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

Annotation

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.

Keywords

distance to boundary, warping function, Payne type inequality, isoperimetric inequality, isoperimetric monotonicity.

The name of the journal

Ufa Mathematical Journal

URL

http://mi.mathnet.ru/ufa475

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

https://repository.kpfu.ru/eng/?p_id=215838&p_lang=2

Resource files

File name	Size (MB)	Format
Salakhudinov_eng.pdf	0,16	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Salakhudinov Rustem Gumerovich	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/eng/?p_id=215838&p_lang=2	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	Articles in Russian journals and collections	ru_RU