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Biharmonic Monogenic Functions and Biharmonic Boundary Value Problems

  • Serhii V. Gryshchuk
  • Sergiy A. Plaksa
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We consider a commutative algebra B over the field of complex numbers with a basis {e1, e2} satisfying the conditions \((e_1^2+e_2^2)^2=0\), \(e_1^2+e_2^2\ne 0\). We consider a Schwarz-type boundary value problem for “analytic” B-valued functions in a simply connected domain. This problem is associated with BVPs for biharmonic functions. Using a hypercomplex analog of the Cauchy type integral, we reduce these BVPs to a system of integral equations on the real axes. We establish sufficient conditions under which this system has the Fredholm property.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Serhii V. Gryshchuk
    • 1
  • Sergiy A. Plaksa
    • 1
  1. 1.Institute of Mathematics, National Academy of Sciences of UkraineKievUkraine

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