A Schwartz-type boundary value problem in a biharmonic plane
- 作者: Gryshchuk S.1, Plaksa S.1
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隶属关系:
- Institute of Mathematics
- 期: 卷 38, 编号 3 (2017)
- 页面: 435-442
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199220
- DOI: https://doi.org/10.1134/S199508021703012X
- ID: 199220
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详细
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.
作者简介
S. Gryshchuk
Institute of Mathematics
编辑信件的主要联系方式.
Email: serhii.gryshchuk@gmail.com
乌克兰, Tereshchenkivska Str. 3, Kiev-4, 01601
S. Plaksa
Institute of Mathematics
Email: serhii.gryshchuk@gmail.com
乌克兰, Tereshchenkivska Str. 3, Kiev-4, 01601