Schwartz-Type Boundary Value Problems for Monogenic Functions in a Biharmonic Algebra

  • S. V. Gryshchuk
  • S. A. Plaksa
Part of the Trends in Mathematics book series (TM)


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 {e1, e2} 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.


Biharmonic equation Biharmonic algebra Biharmonic plane Monogenic function Schwartz-type boundary value problem 

Mathematics Subject Classification (2010)

Primary 30G35; Secondary 31A30 



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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Authors and Affiliations

  • S. V. Gryshchuk
    • 1
  • S. A. Plaksa
    • 1
  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKievUkraine

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