C 1 approximation of functions by solutions of second-order elliptic systems on compact sets in ℝ2

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C ¹ approximation of functions by solutions of second-order elliptic systems on compact sets in ℝ². / Bagapsh, A. O.; Fedorovskiy, K. Yu.

In: Proceedings of the Steklov Institute of Mathematics, Vol. 298, No. 1, 01.08.2017, p. 35-50.

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

BibTeX

@article{045dce2389094915b5b4027099818319,

title = "C 1 approximation of functions by solutions of second-order elliptic systems on compact sets in ℝ2",

abstract = "We consider the problems of C1 approximation of functions by polynomial solutions and by solutions with localized singularities of homogeneous elliptic second-order systems of partial differential equations on compact subsets of the plane ℝ2. We obtain a criterion of C1-weak polynomial approximation which is analogous to Mergelyan{\textquoteright}s criterion of uniform approximability of functions by polynomials in the complex variable. We also discuss the problem of uniform approximation of functions by solutions of the above-mentioned systems. Moreover, we consider the Dirichlet problem for systems that are not strongly elliptic and prove a result on the lack of solvability of such problems for any continuous boundary data in domains whose boundaries contain analytic arcs.",

author = "Bagapsh, {A. O.} and Fedorovskiy, {K. Yu}",

note = "Publisher Copyright: {\textcopyright} 2017, Pleiades Publishing, Ltd.",

year = "2017",

month = aug,

day = "1",

doi = "10.1134/S0081543817060037",

language = "English",

volume = "298",

pages = "35--50",

journal = "Proceedings of the Steklov Institute of Mathematics",

issn = "0081-5438",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "1",

}

RIS

TY - JOUR

T1 - C 1 approximation of functions by solutions of second-order elliptic systems on compact sets in ℝ2

AU - Bagapsh, A. O.

AU - Fedorovskiy, K. Yu

PY - 2017/8/1

Y1 - 2017/8/1

N2 - We consider the problems of C1 approximation of functions by polynomial solutions and by solutions with localized singularities of homogeneous elliptic second-order systems of partial differential equations on compact subsets of the plane ℝ2. We obtain a criterion of C1-weak polynomial approximation which is analogous to Mergelyan’s criterion of uniform approximability of functions by polynomials in the complex variable. We also discuss the problem of uniform approximation of functions by solutions of the above-mentioned systems. Moreover, we consider the Dirichlet problem for systems that are not strongly elliptic and prove a result on the lack of solvability of such problems for any continuous boundary data in domains whose boundaries contain analytic arcs.

AB - We consider the problems of C1 approximation of functions by polynomial solutions and by solutions with localized singularities of homogeneous elliptic second-order systems of partial differential equations on compact subsets of the plane ℝ2. We obtain a criterion of C1-weak polynomial approximation which is analogous to Mergelyan’s criterion of uniform approximability of functions by polynomials in the complex variable. We also discuss the problem of uniform approximation of functions by solutions of the above-mentioned systems. Moreover, we consider the Dirichlet problem for systems that are not strongly elliptic and prove a result on the lack of solvability of such problems for any continuous boundary data in domains whose boundaries contain analytic arcs.

UR - http://www.scopus.com/inward/record.url?scp=85036641664&partnerID=8YFLogxK

U2 - 10.1134/S0081543817060037

DO - 10.1134/S0081543817060037

M3 - Article

AN - SCOPUS:85036641664

VL - 298

SP - 35

EP - 50

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -

ID: 86669176