Abstract:
An explicit representation of the Green function of the Dirichlet problem for the triharmonic equation in the unit ball of space of dimension greater than 2 is given.
Keywords:
Green function, triharmonic equation, Dirichlet problem.
Citation:
V. V. Karachik, “The Green Function of the Dirichlet Problem for the Triharmonic Equation in the Ball”, Mat. Zametki, 107:1 (2020), 87–105; Math. Notes, 107:1 (2020), 105–120
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\paper The Green Function of the Dirichlet Problem for the Triharmonic Equation in the Ball
\jour Mat. Zametki
\yr 2020
\vol 107
\issue 1
\pages 87--105
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\jour Math. Notes
\yr 2020
\vol 107
\issue 1
\pages 105--120
\crossref{https://doi.org/10.1134/S0001434620010101}
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Linking options:
https://www.mathnet.ru/eng/mzm12146
https://doi.org/10.4213/mzm12146
https://www.mathnet.ru/eng/mzm/v107/i1/p87
This publication is cited in the following 17 articles:
V. V. Karachik, “Green's function of one problem for the 3-harmonic equation in a ball”, Complex Variables and Elliptic Equations, 2025, 1
V. V. Karachik, “Green's Function of the Riquier–Neumann Problem for the Polyharmonic Equation in the Unit Ball”, Comput. Math. and Math. Phys., 64:5 (2024), 1015
V. V Karachik, “GREEN'S FUNCTION FOR THE RIEMANN–NEUMANN PROBLEM FOR A POLYHARMONIC EQUATION IN THE UNIT SPHERE”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:5 (2024), 791
Heinrich Begehr, “Green Functions for the Biharmonic Operator”, Lobachevskii J Math, 45:8 (2024), 3488
V. Karachik, “Solvability of the Neumann Boundary Value Problem for the Polyharmonic Equation in a Ball”, Lobachevskii J Math, 45:8 (2024), 3559
V. V. Karachik, “The Green function of the Navier problem for the polyharmonic equation in a ball”, J. Math. Sci., 269:2 (2023), 189
V. Karachik, “Riquier–Neumann problem for the polyharmonic equation in a ball”, Mathematics, 11:4 (2023), 1000
V. Karachik, “On Green's function of the Dirichlet problem for the polyharmonic equation in the ball”, Axioms, 12:6 (2023), 543
V. V. Karachik, “On one integral representation of solutions of polyharmonic equation”, Lobachevskii J. Math., 44:7 (2023), 2749
V. V. Karachik, “Representation of the Green's function of the Dirichlet problem for the polyharmonic equation in the ball”, Diff Equat, 59:8 (2023), 1061
M. Akel, H. Begehr, A. Mohammed, “Integral representations in the complex plane and iterated boundary value problems”, Rocky Mountain J. Math., 52:2 (2022)
V. Karachik, “Green's functions of some boundary value problems for the biharmonic equation”, Complex Variables and Elliptic Equations, 67:7 (2022), 1712
V. V. Karachik, “Solution to the Dirichlet Problem for the Polyharmonic Equation in the Ball”, Sib. Adv. Math., 32:3 (2022), 197
V. V. Karachik, “Reshenie zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share”, Matem. tr., 24:2 (2021), 46–64
V. Karachik, “Dirichlet and Neumann boundary value problems for the polyharmonic equation in the unit ball”, Mathematics, 9:16 (2021), 1907
V. V. Karachik, “Green's functions of the Navier and Riquier-Neumann problems for the biharmonic equation in the ball”, Differ. Equ., 57:5 (2021), 654–668
V. V. Karachik, “Predstavlenie resheniya zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share cherez funktsiyu Grina”, Chelyab. fiz.-matem. zhurn., 5:4(1) (2020), 391–399
Citation in format AMSBIB
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