краевая задача Гильберта

Finding of Accessory Parameters for Mixed Inverse Boundary Value Problem with Polygonal Known Part of Boundary

Authors: Nasyrov S. R., Nizamieva L. Y.

We consider a mixed inverse boundary value problem with respect to parameter x for the case when the known part of the boundary L1z is a polygonal line. Integral representation of solution to the problem depends on real parameters being the pre-images of the vertices of L1z under conformal mapping. By analogy with Schwartz – Christoffel integrals, we name them accessory parameters. It is suggested a new method of determining the accessory parameters.

Certain Caseofthe Riemann–Hilbert Boundary Value Problem with Peculiarities of Coefficients

Authors: Shabalin P. L.

We consider the Riemann – Hilbert boundary value problem for a case where the coefficients have countable set of discontinuity points of the first kind such that the series of jumps of argument of the coefficient function is divergent, but the index of the Hilbert problem is finite. We derive the formulae for general solution of the problem and investigate the picture of solvability.

Modification of new approach to solution of the Hilbert boundary value problem for analytic function in multi-connected circular domain

Authors: Salimov R. B.

The author offers a new approach to the Riemann–Hilbert boundary value problem in multiconnected domain. The approach bases on certain construction of solution of corresponding homogeneous problem including determination of analytic function by known boundary values of its argument circular domain. 

To a Solution of the Inhomogeneous Riemann–Hilbert Boundary Value Problem for Analytic Function in Multiconnected Circular Domain in a Special Case

Authors: Salimov R. B.

The author offers a new approach to solution of the Riemann–Hilbert boundary value problem for analytic function in multiconnected

circular domain. This approach is based on construction of solution of corresponding homogeneous problem, when analytic in domain

function is being defined by known boundary values of its argument. The author considers a special case of a problem when the

index of a problem is more than zero and on unit of less order of connectivity of domain. Resolvability of a problem depends on