The Poincaré Inequality for 3D-Vector Fields and the Neumann Problem

For 3D-vector fields we obtain a family of integral inequalities that can be regarded as the Poincaré inequality within the framework of field theory. We establish a connection between solutions to the corresponding integral identities and the solution to the Neumann problem.

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 281; no. 4; pp. 584 - 594
Main Authors Dubinskii, Yu. A., Zubkov, P. V.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2024
Springer Nature B.V
Subjects
Field theory
Fields (mathematics)
Identities
Mathematics
Mathematics and Statistics
Neumann problem
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Summary:For 3D-vector fields we obtain a family of integral inequalities that can be regarded as the Poincaré inequality within the framework of field theory. We establish a connection between solutions to the corresponding integral identities and the solution to the Neumann problem.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07135-8