Variational field theory from the point of view of direct methods

M. A. Sychev

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

In this paper we show that the classical field theory ofWeierstrass–Hilbert can be strengthen on applying direct methods. Concretely, given a field of extremals and an extremal that is an element of the field, we can show that the latter gives minimum in the class of Lipschitz functions with the same boundary data and with the graphs in the set covered by the field. We suggest the two proofs: a modern one (exploiting Tonelli’s Theorem on lower semicontinuity of integral functionals with respect to the weak convergence of admissible functions in W1,1) and the one based only on arguments available already in the 19th century.

Язык оригиналаанглийский
Страницы (с-по)891-898
Число страниц8
ЖурналSiberian Mathematical Journal
Том58
Номер выпуска5
DOI
СостояниеОпубликовано - 1 сен 2017

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