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IssuesArchive of Issues2020-6pp.808-812

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Total articles in the database: 4918
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Georgievskii D.V., "Second Order Linear Differential Operators over High Rank Tensor Fields," Mech. Solids. 55 (6), 808-812 (2020)
Year 2020 Volume 55 Number 6 Pages 808-812
DOI 10.3103/S0025654420060060
Title Second Order Linear Differential Operators over High Rank Tensor Fields
Author(s) Georgievskii D.V. (Lomonosov Moscow State University, Moscow, 119992 Russia; Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, georgiev@mech.math.msu.su)
Abstract Tensor fields of arbitrary rank in multidimensional space are naturally extended to the concepts of divergence, gradient, curl, deformer operators, as well as their second-order superpositions. Two options for generalizing the rotor as an external product are presented. Differential operators of the second order that do not change the rank of the tensor to which they are applied are considered in detail. Square matrices are introduced, consisting of differential operators Div(l)Grad(k), Grad(k)Div(l), and their relationship is established. An explicit expression is written for the repeated operator rotor. All introduced generalized operators in particular cases agree in their properties with the corresponding classical operators in vector and tensor analysis.
Keywords linear differential operator, divergence, gradient, rotor, Laplacian, deformer, tensor, rank, polyad, Levi-Civita symbol
Received 28 February 2020Revised 11 March 2020Accepted 30 March 2020
Link to Fulltext https://link.springer.com/article/10.3103/S0025654420060060
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