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Article . 2011
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О вариационных уравнениях на пространственных сетях

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2011 Russian Publisher:Федеральное государственное автономное образовательное учреждение высшего образования «Белгородский государственный национальный исследовательский университет»Journal:Научные ведомости Белгородского государственного университета. Серия: Математика. Физика (issn: 1990-5327, Copyright policy )

О вариационных уравнениях на пространственных сетях

Abstract

Устанавливаются аналоги классической теоремы Якоби о положительной определённости второй вариации для функционала, заданного на функциях от ветвящегося аргумента из пространственной сети (геометрического графа). Функционал аналогичен функционалу из задачи Больца. Особенности соответствующего аналога уравнения Якоби (как и уравнения Эйлера) порождены процедурой интегрирования по частям, приводящей к дифференцированию по склеенным (состыкованным) мерам.

Keywords

геометрический граф, вариации функционала, склеенные меры, положительная определённость

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average