Differential Equations

, Volume 55, Issue 2, pp 231–242 | Cite as

On the Hölder Property of Solutions of a Generalized System of Beltrami Equations

  • M. M. SirazhudinovEmail author
  • S. V. Tikhomirova
Partial Differential Equations


We define a generalized Beltrami system, which is a broad generalization of the scalar Beltrami equation to vector equations. The Riemann-Hilbert boundary value problem is considered for such a system under the assumption that it is elliptic (i.e., the roots of the characteristic equation belong to the interior of the unit disk centered at zero). A Cordes type condition on the location of the roots of the characteristic equation of the system is obtained; this is a sufficient condition for the solution of this problem to have the Hölder property. The proof is based on the properties of singular integral operators in a domain.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Dagestan Scientific Center of the Russian Academy of SciencesMakhachkalaRussia
  2. 2.Dagestan State UniversityMakhachkalaRussia
  3. 3.Vladimir State UniversityVladimirRussia

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