Solving the Dirichlet problem for the Lamé system by the hypercomplex method
UDC 517.54, 517.95 A hypercomplex method for solving the Dirichlet problem for the Lamé system in a bounded simply connected domain is developed, which is based on representing solutions via components of a monogenic function in a commutative biharmonic algebra. The Dirichlet problem is reduced to a...
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| Date: | 2026 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9824 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.54, 517.95
A hypercomplex method for solving the Dirichlet problem for the Lamé system in a bounded simply connected domain is developed, which is based on representing solutions via components of a monogenic function in a commutative biharmonic algebra. The Dirichlet problem is reduced to a system of integral equations by using a hypercomplex Cauchy type integral. Sufficient conditions for the Fredholm property of the specified system are established for bounded domains with a smooth boundary belonging to a class essentially wider than the class of Lyapunov curves, in the case where the given boundary functions belong to wider classes than the H\"older classes. The solution of the Dirichlet problem for a disk is obtained in explicit form. |
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| DOI: | 10.3842/umzh.v78i5-6.9824 |