Standard

Uniform and C1-approximability of functions on compact subsets of ℝ2 by solutions of second-order elliptic equations. / Paramonov, P. V.; Fedorovskiǐ, K. Yu.

In: Sbornik Mathematics, Vol. 190, No. 1-2, 1999, p. 285-307.

Research output: Contribution to journal › Article › peer-review

Harvard

Paramonov, PV & Fedorovskiǐ, KY 1999, 'Uniform and C1-approximability of functions on compact subsets of ℝ2 by solutions of second-order elliptic equations', Sbornik Mathematics, vol. 190, no. 1-2, pp. 285-307. https://doi.org/10.1070/sm1999v190n02abeh000386

APA

Paramonov, P. V., & Fedorovskiǐ, K. Y. (1999). Uniform and C1-approximability of functions on compact subsets of ℝ2 by solutions of second-order elliptic equations. Sbornik Mathematics, 190(1-2), 285-307. https://doi.org/10.1070/sm1999v190n02abeh000386

Vancouver

Paramonov PV, Fedorovskiǐ KY. Uniform and C1-approximability of functions on compact subsets of ℝ2 by solutions of second-order elliptic equations. Sbornik Mathematics. 1999;190(1-2):285-307. https://doi.org/10.1070/sm1999v190n02abeh000386

Author

Paramonov, P. V. ; Fedorovskiǐ, K. Yu. / Uniform and C1-approximability of functions on compact subsets of ℝ2 by solutions of second-order elliptic equations. In: Sbornik Mathematics. 1999 ; Vol. 190, No. 1-2. pp. 285-307.

BibTeX

@article{dfb3cd068102450292d45f7f3306d276,
title = "Uniform and C1-approximability of functions on compact subsets of ℝ2 by solutions of second-order elliptic equations",
abstract = "Several necessary and sufficient conditions for the existence of uniform or C1-approximation of functions on compact subsets of ℝ2 by solutions of elliptic systems of the form c11ux1x1 + 2c12ux1x2 + c22ux2x2 = 0 with constant complex coefficients c11, c12, and c22 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.",
author = "Paramonov, {P. V.} and Fedorovskiǐ, {K. Yu}",
year = "1999",
doi = "10.1070/sm1999v190n02abeh000386",
language = "English",
volume = "190",
pages = "285--307",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Turpion Ltd.",
number = "1-2",

}

RIS

TY - JOUR

T1 - Uniform and C1-approximability of functions on compact subsets of ℝ2 by solutions of second-order elliptic equations

AU - Paramonov, P. V.

AU - Fedorovskiǐ, K. Yu

PY - 1999

Y1 - 1999

N2 - Several necessary and sufficient conditions for the existence of uniform or C1-approximation of functions on compact subsets of ℝ2 by solutions of elliptic systems of the form c11ux1x1 + 2c12ux1x2 + c22ux2x2 = 0 with constant complex coefficients c11, c12, and c22 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.

AB - Several necessary and sufficient conditions for the existence of uniform or C1-approximation of functions on compact subsets of ℝ2 by solutions of elliptic systems of the form c11ux1x1 + 2c12ux1x2 + c22ux2x2 = 0 with constant complex coefficients c11, c12, and c22 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.

UR - http://www.scopus.com/inward/record.url?scp=0033451151&partnerID=8YFLogxK

U2 - 10.1070/sm1999v190n02abeh000386

DO - 10.1070/sm1999v190n02abeh000386

M3 - Article

AN - SCOPUS:0033451151

VL - 190

SP - 285

EP - 307

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 1-2

ER -

ID: 86670029