We consider a commutative algebra over the field of complex numbers with a basis e1, e2 satisfying the conditions [...] (e12+e22)2=0,e12+e22≠0. Let D be a bounded simply-connected domain in ℝ2. We consider (1-4)-problem for monogenic -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.
@article{bwmeta1.element.doi-10_1515_math-2017-0025,
author = {Serhii V. Gryshchuk and Sergiy A. Plaksa},
title = {Reduction of a Schwartz-type boundary value problem for biharmonic monogenic functions to Fredholm integral equations},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {374-381},
zbl = {06704091},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0025}
}
Serhii V. Gryshchuk; Sergiy A. Plaksa. Reduction of a Schwartz-type boundary value problem for biharmonic monogenic functions to Fredholm integral equations. Open Mathematics, Tome 15 (2017) pp. 374-381. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0025/