Abstract
For a strongly elliptic system of second-order equations of a special form, formulas for the Poisson integral and Green’s function in a circle and an ellipse are obtained. The operator under consideration is represented by the sum of the Laplacian and a residual part with a small parameter, and the solution to the Dirichlet problem is found in the form of a series in powers of this parameter. The Poisson formula is obtained by the summation of this series.
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Original Russian Text © A.O. Bagapsh, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 12, pp. 2065–2072.
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Bagapsh, A.O. The Poisson integral and Green’s function for one strongly elliptic system of equations in a circle and an ellipse. Comput. Math. and Math. Phys. 56, 2035–2042 (2016). https://doi.org/10.1134/S0965542516120046
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DOI: https://doi.org/10.1134/S0965542516120046