Geodesic
The Poisson integral and Green's function for one strongly elliptic system of equations in a circle and an ellipse
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2065-2072

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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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     author = {A. O. Bagapsh},
     title = {The {Poisson} integral and {Green's} function for one strongly elliptic system of equations in a circle and an ellipse},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2065--2072},
     publisher = {mathdoc},
     volume = {56},
     number = {12},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a6/}
}
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A. O. Bagapsh. The Poisson integral and Green's function for one strongly elliptic system of equations in a circle and an ellipse. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2065-2072. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a6/