On the fundamental solution matrix of the plane anisotropic elasticity theory. (English. Russian original) Zbl 1522.74010
Differ. Equ. 59, No. 5, 646-653 (2023); translation from Differ. Uravn. 59, No. 5, 635-641 (2023).
Summary: An explicit expression (in polar coordinates) for the fundamental solution matrix of the Lamé system of the plane anisotropic theory of elasticity is given. It is shown that the operator of convolution with this matrix in a finite domain with Lyapunov boundary is bounded in the Hölder spaces \(C^\mu \to C^{2,\mu } \). A similar result is also established for an infinite domain in the corresponding weighted Hölder spaces (with a power-law behavior at infinity).
MSC:
| 74B05 | Classical linear elasticity |
| 74E10 | Anisotropy in solid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
polar coordinates; Lamé system; convolution operator; boundedness; Lyapunov boundary; weighted Hoelder spaceReferences:
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| [5] | Otelbaev, M.; Soldatov, A. P., integral representations of vector functions based on the parametrix of first-order elliptic systems, Comput. Math. Math. Phys., 61, 1, 964-973 (2021) · Zbl 1472.35091 · doi:10.1134/S0965542521030143 |
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