Singular Riemann–Hilbert problem in complex shaped domainsстатья
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Дата последнего поиска статьи во внешних источниках: 12 января 2015 г.
Аннотация:In simply connected domains of complex geometry, a Riemann – Hilbert problem with
discontinuous data and a solution growing at some points of the boundary is considered. The desired analytic function F (z) is represented as the composition of a conformal mapping of onto the half plane H and the solution P of the corresponding Riemann – Hilbert problem in H. Methods for finding this mapping are described, and a technique for constructing an analytic function P in H in the terms of a modified Cauchytype integral. In the case of piecewise constant data of the problem, a fundamentally new representation of P in the form of a Christoffel – Schwarz type integral is obtained, which solves the Riemann problem of a geometric interpretation of the solution and is more convenient for numerical implementation than the conventional representation in terms of Cauchy type integrals.