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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm386https://doi.org/10.1070/sm1999v190n02ABEH000386 https://www.mathnet.ru/eng/sm/v190/i2/p123
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