 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 55, Issue 6 / 2020 | Next article >> |
| 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 2020 | Revised |
11 March 2020 | Accepted |
30 March 2020 |
| Link to Fulltext |
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