Abstract
It is proved that an equilateral triangle is the unique polygon on which the solution of the equation Δu=1 with homogeneous boundary conditions is an algebraic polynomial, and moreover, the degree of this polynomial is equal to 3.
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References
L. I. Sedov,Mechanics of Continuous Media [in Russian], Vol. 2, Nauka, Moscow (1994).
E. A. Volkov, “On differential properties of solutions to boundary values problems for the Laplace equation on polygons,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],77, 113–142 (1965).
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Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 178–180, August, 1999.
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Volkov, E.A. On a property of solutions to the poisson equation on polygons. Math Notes 66, 139–141 (1999). https://doi.org/10.1007/BF02674868
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DOI: https://doi.org/10.1007/BF02674868