Abstract
We consider Schwartz-type boundary value problems for monogenic functions in a commutative algebra \(\mathbb {B}\) over the field of complex numbers with the bases {e 1, e 2} satisfying the conditions \((e_1^2+e_2^2)^2=0\), \(e_1^2+e_2^2\ne 0\). The algebra \(\mathbb {B}\) is associated with the biharmonic equation, and considered problems have relations to the plane elasticity. We develop methods of its solving which are based on expressions of solutions by hypercomplex integrals analogous to the classic Schwartz and Cauchy integrals.
Dedicated to Professor Heinrich G.W. Begher on the occasion of his 80th birthday
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Acknowledgements
This research is partially supported by the State Program of Ukraine (Project No. 0117U004077) and Grant of Ministry of Education and Science of Ukraine (Project No. 0116U001528).
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Gryshchuk, S.V., Plaksa, S.A. (2019). Schwartz-Type Boundary Value Problems for Monogenic Functions in a Biharmonic Algebra. In: Rogosin, S., Çelebi, A. (eds) Analysis as a Life. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02650-9_10
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DOI: https://doi.org/10.1007/978-3-030-02650-9_10
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