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

Serhii V. GryshchukSergiy A. Plaksa — 2017

Open Mathematics

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. ( e 1 2 + e 2 2 ) 2 = 0 , e 1 2 + e 2 2 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...

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