Geodesic
Approximate solution of the Dirichlet problem in a circle
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 83-91
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The approaches to the solution of Dirichlet problem in a unit radius circle are constructed in the manner of rational functions. There were found the estimates of approaches' inaccuracies. Assuming that the boundary condition is to be a measurable bounded function with the finite number of discontinuities. Constructions use the solution of trigonometric problem of moments. 
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Alexander Kouleshoff. Approximate solution of the Dirichlet problem in a circle. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 83-91. http://geodesic.mathdoc.fr/item/BASM_2003_3_a7/

[1] Szegö G., Orthogonal polynomials, New York, 1939

[2] Nikishin E. M., Sorokin V. N., Rational approximations and orthogonal, Nauka, Moscow, 1988, 112–144. | MR | Zbl

[3] Geronimus Ya. L., Polynomials orthogonal on the circle and on the segment, Phizmatgiz, Moscow, 1958