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Sbornik: Mathematics, 1999, Volume 190, Issue 2, Pages 285–307
DOI: https://doi.org/10.1070/sm1999v190n02ABEH000386
(Mi sm386)
 

This article is cited in 30 scientific papers (total in 30 papers)

Uniform and $C^1$-approximability of functions on compact subsets of $\mathbb R^2$ by solutions of second-order elliptic equations

P. V. Paramonova, K. Yu. Fedorovskiyb

a M. V. Lomonosov Moscow State University
b Institute of Information Systems in Management at the State University of Management
References:
Abstract: Several necessary and sufficient conditions for the existence of uniform or $C^1$-approximation of functions on compact subsets of $\mathbb R^2$ by solutions of elliptic systems of the form $c_{11}u_{x_1x_1}+2c_{12}u_{x_1x_2}+c_{22}u_{x_2x_2}=0$ with constant complex coefficients $c_{11}$, $c_{12}$ and $c_{22}$ are obtained. The proofs are based on a refinement of Vitushkin's localization method, in which one constructs localized approximating functions by “gluing together” some special many-valued solutions of the above equations. The resulting conditions of approximation are of a topological and metric nature.
Received: 21.06.1996 and 02.06.1998
Bibliographic databases:
UDC: 517.538.5+517.956.22
MSC: 30E10, 35J15
Language: English
Original paper language: Russian
Citation: P. V. Paramonov, K. Yu. Fedorovskiy, “Uniform and $C^1$-approximability of functions on compact subsets of $\mathbb R^2$ by solutions of second-order elliptic equations”, Sb. Math., 190:2 (1999), 285–307
Citation in format AMSBIB
\Bibitem{ParFed99}
\by P.~V.~Paramonov, K.~Yu.~Fedorovskiy
\paper Uniform and $C^1$-approximability of functions on compact subsets of $\mathbb R^2$ by solutions of second-order elliptic equations
\jour Sb. Math.
\yr 1999
\vol 190
\issue 2
\pages 285--307
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\crossref{https://doi.org/10.1070/sm1999v190n02ABEH000386}
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\zmath{https://zbmath.org/?q=an:1052.30038}
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  • https://doi.org/10.1070/sm1999v190n02ABEH000386
  • https://www.mathnet.ru/eng/sm/v190/i2/p123
  • This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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