Variational field theory from the point of view of direct methods
- 作者: Sychev M.1
-
隶属关系:
- Sobolev Institute of Mathematics
- 期: 卷 58, 编号 5 (2017)
- 页面: 891-898
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171498
- DOI: https://doi.org/10.1134/S0037446617050160
- ID: 171498
如何引用文章
详细
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.
作者简介
M. Sychev
Sobolev Institute of Mathematics
编辑信件的主要联系方式.
Email: masychev@math.nsc.ru
俄罗斯联邦, Novosibirsk