Approximation of Hölder Functions in the Lp Norm by Harmonic Functions on Some Multidimensional Compact Sets

In this paper, the class of Hölder functions in the sense of the L p norm on certain compacts in ( m 3) is analyzed, and theorems of the approximation by functions being harmonic in the neighborhoods of these compacts are proved. These compacts represent a generalization of the concept of a chord-ar...

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Published in:Vestnik, St. Petersburg University. Mathematics St. Petersburg University. Mathematics, 2023, Vol.56 (2), p.190-197
Main Author: Pavlov, D. A.
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Language:English
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Analysis
Approximation
Compacts
Harmonic functions
Mathematical analysis
Mathematics
Mathematics and Statistics
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description In this paper, the class of Hölder functions in the sense of the L p norm on certain compacts in ( m 3) is analyzed, and theorems of the approximation by functions being harmonic in the neighborhoods of these compacts are proved. These compacts represent a generalization of the concept of a chord-arc curve in to higher dimensions. The neighborhood size decreases along with an increase in the approximation accuracy. Estimates of the approximation rate as well as the gradient of the approximation functions are made in the same L p norm.
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subjects Analysis
Approximation
Compacts
Harmonic functions
Mathematical analysis
Mathematics
Mathematics and Statistics
title Approximation of Hölder Functions in the Lp Norm by Harmonic Functions on Some Multidimensional Compact Sets
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