Uniform approximation of functions by solutions of strongly elliptic equations of second order on compact subsets of

DOI10.1070/SM9503zbMath1500.35010OpenAlexW3206651815MaRDI QIDQ3391031

Peter V. Paramonov

Publication date: 28 March 2022

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm9503

zbMATH Keywords

uniform approximationmethod of reduction\(L\)-capacity\(L\)-oscillationstrongly elliptic equations of second orderVitushkin-type localization operator

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Second-order elliptic equations (35J15) Theoretical approximation in context of PDEs (35A35) Approximation by other special function classes (41A30)

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Uniform approximation by polynomial solutions of elliptic systems on boundaries of Carathéodory domains in \(\mathbb{R}^2\) ⋮ Explicit form of fundamental solutions to certain elliptic equations and associated $B$- and $C$-capacities

Cites Work

• \(C^ m\) approximation by solutions of elliptic equations, and Calderón-Zygmund operators
• New criteria for uniform approximability by harmonic functions on compact sets in \(\mathbb{R}^2\)
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• Uniform and $ C^1$-approximability of functions on compact subsets of $ \mathbb R^2$ by solutions of second-order elliptic equations
• Estimates for potentials and $ \delta$-subharmonic functions outside exceptional sets
• Criteria for the individual $C^m$-approximability of functions on compact subsets of $ {\mathbb R}^N$ by solutions of second-order homogeneous elliptic equations
• Approximation by Solutions of Elliptic Equations on Closed Subsets of Euclidean Space.
• Conditions for $ C^m$-approximability of functions by solutions of elliptic equations
• Criteria for -approximability of functions on compact sets in , , by solutions of second-order homogeneous elliptic equations
• A criterion for uniform approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients
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