A Schwartz-type boundary value problem in a biharmonic plane
- Autores: Gryshchuk S.1, Plaksa S.1
-
Afiliações:
- Institute of Mathematics
- Edição: Volume 38, Nº 3 (2017)
- Páginas: 435-442
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199220
- DOI: https://doi.org/10.1134/S199508021703012X
- ID: 199220
Citar
Resumo
A commutative algebra B over the field of complex numbers with the bases {e1, e2} satisfying the conditions (e12 + e22)2 = 0, e12 + e22)2 ≠ 0, is considered. The algebra B is associated with the biharmonic equation. Consider a Schwartz-type boundary value problem on finding a monogenic function of the type Φ(xe1 + ye2) = U1(x, y)e1 + U2(x, y)ie1 + U3(x, y)e2 + U4(x, y)ie2, (x, y) ∈ D, when values of two components U1, U4 are given on the boundary of a domain D lying in the Cartesian plane xOy. We develop a method of its solving which is based on expressions of monogenic functions via corresponding analytic functions of the complex variable. For a half-plane and for a disk, solutions are obtained in explicit forms by means of Schwartz-type integrals.
Sobre autores
S. Gryshchuk
Institute of Mathematics
Autor responsável pela correspondência
Email: serhii.gryshchuk@gmail.com
Ucrânia, Tereshchenkivska Str. 3, Kiev-4, 01601
S. Plaksa
Institute of Mathematics
Email: serhii.gryshchuk@gmail.com
Ucrânia, Tereshchenkivska Str. 3, Kiev-4, 01601