Singular Riemann-Hilbert problem in complex-shaped domains

On a Problem of the Constructive Theory of Harmonic Mappings

“…The solution of this (nonclassical) Dirichlet problem can be written in the following form, which follows from the results of [14,15]:…”

“…Using the results of [14,15] for the Riemann-Hilbert problem, we obtain the solution of problem (3.30)- (3.32) in the form…”

“…2. A high-precision solution of the Roache-Steinberg problem obtained by the multipole method combined with results from [14,15] is given in Sec. 3.…”

On capacity computation for symmetric polygonal condensers

“…This method of capacity computation is based on using the SC integral technique [BeV1,BeV2] in combination with new results on the Lauricella function theory [Be1,Be2,Be3]. In the mentioned works the method was successfully applied to conformal mapping of a number of complex-shaped domains with highly efficient solution of parameter problem for the SC integral in crowding situation (very close location of pre-vertices).…”

“…For a number of elaborate domains [BeV1,BeV2], it was found a good initial approximation for system (9) of transcendental equation for parameters of the SC integral. It was made by application of the theory of conformal mapping of singularly deformed domains.…”