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• # Artykuł - szczegóły

## Open Mathematics

2017 | 15 | 1 | 374-381

## Reduction of a Schwartz-type boundary value problem for biharmonic monogenic functions to Fredholm integral equations

EN

### Abstrakty

EN
We consider a commutative algebra 𝔹 over the field of complex numbers with a basis {e1, e2} satisfying the conditions [...] (e12+e22)2=0,e12+e22≠0. $(e_{1}^{2}+e_{2}^{2})^{2}=0, e_{1}^{2}+e_{2}^{2}\neq 0.$ Let D be a bounded simply-connected domain in ℝ2. We consider (1-4)-problem for monogenic 𝔹-valued functions Φ(xe1 + ye2) = U1(x, y)e1 + U2(x, y)i e1 + U3(x, y)e2 + U4(x, y)i e2 having the classic derivative in the domain Dζ = {xe1 + ye2 : (x, y) ∈ D}: to find a monogenic in Dζ function Φ, which is continuously extended to the boundary ∂Dζ, when values of two component-functions U1, U4 are given on the boundary ∂D. Using a hypercomplex analog of the Cauchy type integral, we reduce the (1-4)-problem to a system of integral equations on the real axes. We establish sufficient conditions under which this system has the Fredholm property and the unique solution. We prove that a displacements-type boundary value problem of 2-D isotropic elasticity theory is reduced to (1-4)-problem with appropriate boundary conditions.

EN

374-381

wydano
2017-01-01
otrzymano
2016-10-22
zaakceptowano
2017-02-12
online
2017-04-01

### Twórcy

autor
• Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska Str. 3, 01004, Kiev-4,
autor
• Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska Str. 3, 01004, Kiev-4,