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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2001, Volume 232, Pages 102–114 (Mi tm207)  
On the Solvability, in the Class of Polynomials, of the Dirichlet Problem for the Laplace Equation on an Arbitrary Polygon

E. A. Volkov
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Abstract: A constructive algorithm is developed that distinguishes between the cases when the solution to the Dirichlet problem for the Laplace equation is or is not a harmonic polynomial when the boundary values on the sides of an arbitrary polygon are specified by algebraic polynomials.
Received in August 2000
Bibliographic databases:
Document Type: Article
UDC: 517.956.2
Language: Russian
Citation: E. A. Volkov, “On the Solvability, in the Class of Polynomials, of the Dirichlet Problem for the Laplace Equation on an Arbitrary Polygon”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 232, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 102–114; Proc. Steklov Inst. Math., 232 (2001), 96–108
Citation in format AMSBIB
\Bibitem{Vol01}
\by E.~A.~Volkov
\paper On the Solvability, in the Class of Polynomials, of the Dirichlet Problem for the Laplace Equation on an Arbitrary Polygon
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 102--114
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm207}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1851443}
\zmath{https://zbmath.org/?q=an:1253.35049}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 96--108
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