3D Vector Field Formula and an Analog of the Neumann Problem in Field Theory

被引：0
|
作者：
Dubinskii Y.A. [1 ]
机构：
[1] National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya St, Moscow
来源：
Journal of Mathematical Sciences | 2022年 / 267卷 / 3期
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D O I：
10.1007/s10958-022-06138-7
中图分类号：
学科分类号：
摘要：
We obtain a necessary and sufficient condition for the relation ‖∇u‖2 = ‖curl u‖2 + ‖div u‖2 between the main operations of field theory (gradient, curl, and divergence) on the boundary of a domain. As an application, we consider an analog of the classical Neumann problem in field theory and find a condition on the right-hand side of the equation for a weak solution to be a generalized solution. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.
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页码：362 / 369
页数：7
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