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 Tr. Mat. Inst. Steklova, 2006, Volume 253, Pages 67–80 (Mi tm84)

Uniform Approximation by Polynomial Solutions of Second-Order Elliptic Equations, and the Corresponding Dirichlet Problem

A. B. Zaitsev

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)

Abstract: Conditions for the uniform approximability of functions by polynomial solutions of second-order elliptic equations with constant complex coefficients on compact sets of special form in $\mathbb R^2$ are studied. The results obtained are of analytic character. Conditions of solvability and uniqueness for the corresponding Dirichlet problem are also studied. It is proved that the polynomial approximability on the boundary of a domain is not generally equivalent to the solvability of the corresponding Dirichlet problem.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 253, 57–70

Bibliographic databases:

UDC: 517.538.5+517.956.2

Citation: A. B. Zaitsev, “Uniform Approximation by Polynomial Solutions of Second-Order Elliptic Equations, and the Corresponding Dirichlet Problem”, Complex analysis and applications, Collected papers, Tr. Mat. Inst. Steklova, 253, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 67–80; Proc. Steklov Inst. Math., 253 (2006), 57–70

Citation in format AMSBIB
\Bibitem{Zai06} \by A.~B.~Zaitsev \paper Uniform Approximation by Polynomial Solutions of Second-Order Elliptic Equations, and the Corresponding Dirichlet Problem \inbook Complex analysis and applications \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2006 \vol 253 \pages 67--80 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm84} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338688} \elib{http://elibrary.ru/item.asp?id=13508457} \transl \jour Proc. Steklov Inst. Math. \yr 2006 \vol 253 \pages 57--70 \crossref{https://doi.org/10.1134/S0081543806020064} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748311911} 

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This publication is cited in the following articles:
1. K. Yu. Fedorovskiy, “On $\mathcal C^m$-approximability of functions by polynomial solutions of elliptic equations on compact plane sets”, St. Petersburg Math. J., 24:4 (2013), 677–689
2. A. O. Bagapsh, K. Yu. Fedorovskiy, “$C^1$ Approximation of Functions by Solutions of Second-Order Elliptic Systems on Compact Sets in $\mathbb R^2$”, Proc. Steklov Inst. Math., 298 (2017), 35–50
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