REPRESENTATION OF THE GREEN’S FUNCTION OF THE NAVIER PROBLEM FOR THE BIHARMONIC EQUATION IN A BALL

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Resumo

The paper presents a new representation of the Green’s function of the Navier problem for the biharmonic equation in the unit ball and gives a representation of the solution of the Navier problem for the homogeneous biharmonic equation without explicit use of the Green’s function.

Sobre autores

V. Karachik

South Ural State University (National Research University)

Email: karachik@susu.ru
Chelyabinsk, Russia

Bibliografia

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  3. Ying, W. Tri-harmonic boundary value problems in a sector / W. Ying // Complex Variables and Elliptic Equations. — 2014. — V. 59, № 5. — P. 732–749.
  4. Karachik, V.V. Green’s function of Dirichlet problem for biharmonic equation in the ball / V.V. Karachik // Complex Variables and Elliptic Equations. — 2019. — V. 64, № 9. — P. 1500–1521.
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  7. Карачик, В.В. Функции Грина задач Навье и Рикье–Неймана для бигармонического уравнения в шаре / В.В. Карачик // Дифференц. уравнения. — 2021. — Т. 57, № 5. — С. 673–686.
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  10. Gazzola, F. Polyharmonic Boundary Value Problems / F. Gazzola, H.C. Grunau, G. Sweers. — Springer, 2010. — 429 p.
  11. Karachik, V.V. On some special polynomials / V.V. Karachik // Proc. Amer. Math. Soc. — 2004. — V. 132, № 4. — P. 1049–1058.
  12. Karachik, V.V. Dirichlet and Neumann boundary value problems for the polyharmonic equation in the unit ball / V.V. Karachik // Mathematics. — 2021. — V. 9, № 16. — Art. 1907.
  13. Karachik, V.V. Green’s functions of some boundary value problems for the biharmonic equation / V.V. Karachik // Complex Variables and Elliptic Equations. — 2022. — V. 67, № 7. — P. 1712–1736.

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