Summary
The Dirichlet problem is solved for an elliptic domain if the boundary values are given by a polynomial defined in the interior of the ellipse. The solution is a finite expansion in harmonic polynomials.
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Vodička, V. Elementare Fälle des Dirichletschen Problems für elliptische Gebiete der Ebene. Journal of Applied Mathematics and Physics (ZAMP) 8, 309–313 (1957). https://doi.org/10.1007/BF01600620
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DOI: https://doi.org/10.1007/BF01600620