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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 301, Pages 7–17
DOI: https://doi.org/10.1134/S0371968518020012 (Mi tm3916) 		 
This article is cited in 1 scientific paper (total in 1 paper)

$C^m$ approximation of functions by solutions of second-order elliptic systems on compact sets in the plane

A. O. Bagapshab, K. Yu. Fedorovskiyac

a Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5/1, Moscow, 105005 Russia
b Dorodnicyn Computing Centre, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
c Mathematics and Mechanics Faculty, St. Petersburg State University, Universitetskii pr. 28, Peterhof, St. Petersburg, 198504 Russia
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DOI: https://doi.org/10.1134/S0371968518020012
Abstract: This paper is a brief survey of the recent results in problems of approximating functions by solutions of homogeneous elliptic systems of PDEs on compact sets in the plane in the norms of $C^m$ spaces, $m\geq0$. We focus on general second-order systems. For such systems the paper complements the recent survey by M. Mazalov, P. Paramonov, and K. Fedorovskiy (2012), where the problems of $C^m$ approximation of functions by holomorphic, harmonic, and polyanalytic functions as well as by solutions of homogeneous elliptic PDEs with constant complex coefficients were considered.
Keywords: elliptic equation, second-order elliptic system, $C^m$ approximation, $\kappa _{m,\tau ,\sigma }$-capacity, $s$-dimensional Hausdorff content, Vitushkin localization operator.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.517.2016/1.4
1.3843.2017/4.6
Russian Foundation for Basic Research 16-01-00781
18-01-00764
Simons Foundation Simons-IUM fellowship
The research was supported by the Ministry of Education and Science of the Russian Federation (project nos. 1.517.2016/1.4 (second author) and 1.3843.2017/4.6) and by the Russian Foundation for Basic Research (project nos. 16-01-00781 and 18-01-00764). The second author was also supported by the Simons Foundation (Simons–IUM fellowship).
Received: January 31, 2018
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 301, Pages 1–10
DOI: https://doi.org/10.1134/S0081543818040016
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. O. Bagapsh, K. Yu. Fedorovskiy, “$C^m$ approximation of functions by solutions of second-order elliptic systems on compact sets in the plane”, Complex analysis, mathematical physics, and applications, Collected papers, Trudy Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 7–17; Proc. Steklov Inst. Math., 301 (2018), 1–10
Citation in format AMSBIB
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\pages 7--17
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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