KFU. Card publication. Payne type inequalities for $L^p$--norms of the warping functions

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PAYNE TYPE INEQUALITIES FOR $L^P$--NORMS OF THE WARPING FUNCTIONS

Form of presentation

Articles in international journals and collections

Year of publication

2014

Authors, employees of KFU

Salakhudinov Rustem Gumerovich, author

Bibliographic description in the original language

Salakhudinov R.G. Payne type inequalities for $L^p$--norms of the warping functions // J. of Math. Anal. and Appl. - 2014.- Vol. 410. - No. 2. - P. 659-669. DOI: 10.1016/j.jmaa.2013.08.042

Annotation

J MATH ANAL APPL

Keywords

warping function, torsional rigidity, isoperimetric inequality, Payne's inequality, isoperimetric monotonicity, symmetrization

The name of the journal

J MATH ANAL APPL

URL

http://www.sciencedirect.com/science/article/pii/S0022247X13007828

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

https://repository.kpfu.ru/eng/?p_id=78751&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Salakhudinov Rustem Gumerovich	ru_RU
dc.date.accessioned	2014-01-01T00:00:00Z	ru_RU
dc.date.available	2014-01-01T00:00:00Z	ru_RU
dc.date.issued	2014	ru_RU
dc.identifier.citation	Salakhudinov R.G. Payne type inequalities for $L^p$--norms of the warping functions // J. of Math. Anal. and Appl. - 2014.- Vol. 410. - No. 2. - P. 659-669. DOI: 10.1016/j.jmaa.2013.08.042	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=78751&p_lang=2	ru_RU
dc.description.abstract	J MATH ANAL APPL	ru_RU
dc.description.abstract	J MATH ANAL APPL	ru_RU
dc.description.abstract	Let $u(x,G)$ be a warping function of a multiply connected plane domain $G$. A new physical functional of $u(x,G)$ with an isoperimetric monotonicity property is constructed. It is proved that $L^p$ and $L^q$ norms of the warping function satisfy sharp isoperimetric inequalities, which, besides the norms, can contain the functional $\supu{G}=\sup_{x\in G}u(x,G)$. As a particular case of one of these inequalities it follows the classical result of Payne for the torsional rigidity of $G$. Our proofs are based on the technique of estimates on level lines devised by L. E. Payne.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	warping function	ru_RU
dc.subject	torsional rigidity	ru_RU
dc.subject	isoperimetric inequality	ru_RU
dc.subject	Payne's inequality	ru_RU
dc.subject	isoperimetric monotonicity	ru_RU
dc.subject	symmetrization	ru_RU
dc.title	Payne type inequalities for $L^p$--norms of the warping functions	ru_RU
dc.type	Articles in international journals and collections	ru_RU