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Differential Equations on Complex Manifolds

  • Anton Savin
  • Boris Sternin
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We discuss linear partial differential equations with constant coefficients on complex manifold \( \mathbb{C}^n \). Using the Sternin–Shatalov integral transform we solve complex Cauchy problem and consider two applications: describe the singularities of the solution of the Cauchy problem and solve a physical problem of sweeping the charge inside the domain (balayage inwards problem).

Keywords

complex theory of differential equations Cauchy problem balayage inwards propagation of singularities Landau manifold integral transform 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia
  2. 2.Institut für AnalysisLeibniz University of HannoverHannoverGermany

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