Abstract:
A set of necessary solvability conditions for the class ${\mathcal{N}}_{k}$ of Neumann-type problems for the polyharmonic equation with a polynomial right-hand side in the unit ball is obtained. These conditions have the form of the orthogonality of homogeneous harmonic polynomials to linear combinations of boundary functions with coefficients from the Neumann integer triangle perturbed by certain derivatives of the right-hand side of the equation.
Citation:
V. V. Karachik, “Class of Neumann-type problems for the polyharmonic equation in a ball”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 132–150; Comput. Math. Math. Phys., 60:1 (2020), 144–162
\Bibitem{Kar20}
\by V.~V.~Karachik
\paper Class of Neumann-type problems for the polyharmonic equation in a ball
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 1
\pages 132--150
\mathnet{http://mi.mathnet.ru/zvmmf11024}
\crossref{https://doi.org/10.31857/S0044466919120123}
\elib{https://elibrary.ru/item.asp?id=41806932}
\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 1
\pages 144--162
\crossref{https://doi.org/10.1134/S096554251912011X}
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Linking options:
https://www.mathnet.ru/eng/zvmmf11024
https://www.mathnet.ru/eng/zvmmf/v60/i1/p132
This publication is cited in the following 7 articles:
A. Darya, N. Taghizadeh, “Three Boundary Value Problems for Complex Partial Differential Equations in the Lens Domain”, Comput. Math. and Math. Phys., 64:6 (2024), 1295
B. Turmetov, V. Karachik, M. Muratbekova, “On a boundary value problem for the biharmonic equation with multiple involutions”, Mathematics, 9:17 (2021), 2020
Batirkhan Turmetov, Valery Karachik, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2365, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021, 060002
V. V. Karachik, “Sufficient conditions for solvability of one class of Neumann-type problems for the polyharmonic equation”, Comput. Math. Math. Phys., 61:8 (2021), 1276–1288
H. A. Matevossian, “Biharmonic problem with Dirichlet and Steklov-type boundary conditions in weighted spaces”, Comput. Math. Math. Phys., 61:6 (2021), 938–952
V. V. Karachik, “Usloviya razreshimosti zadachi Neimana $\mathcal{N}_2$ dlya poligarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 12:2 (2020), 13–20
H. A. Matevossian, “Asymptotics and uniqueness of solutions of the elasticity system with the mixed dirichlet-robin boundary conditions”, Mathematics, 8:12 (2020), 2241
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