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This article is cited in 3 scientific papers (total in 3 papers)
Partial Differential Equations
Sufficient conditions for solvability of one class of Neumann-type problems for the polyharmonic equation
V. V. Karachik South Ural State University, 454080, Chelyabinsk, Russia
Abstract:
The solvability of one class of Neumann-type problems for the homogeneous polyharmonic equation in the unit ball is investigated. First, local sufficient conditions for the solvability of Neumann-type problems are obtained; then they are transformed to boundary conditions in integral form as conditions of orthogonality on the unit sphere of homogeneous harmonic polynomials of some degrees to linear combinations of boundary functions with coefficients from the integer Neumann triangle. These sufficient conditions are identical to the previously obtained set of necessary conditions for the solvability of the Neumann-type problems under consideration. An example is considered.
Key words:
polyharmonic equation, necessary and sufficient conditions, solvability, Neumann-type problems.
Received: 24.06.2020 Revised: 12.11.2020 Accepted: 16.12.2020
Citation:
V. V. Karachik, “Sufficient conditions for solvability of one class of Neumann-type problems for the polyharmonic equation”, Zh. Vychisl. Mat. Mat. Fiz., 61:8 (2021), 1295–1308; Comput. Math. Math. Phys., 61:8 (2021), 1276–1288
Linking options:
https://www.mathnet.ru/eng/zvmmf11277 https://www.mathnet.ru/eng/zvmmf/v61/i8/p1295
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