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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Bibliographic Details
Published in:Vestnik, St. Petersburg University. Mathematics St. Petersburg University. Mathematics, 2023, Vol.56 (2), p.190-197
Main Author: Pavlov, D. A.
Format: Article
Language:English
Subjects:
Analysis
Approximation
Compacts
Harmonic functions
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1063-4541
1934-7855
DOI:10.1134/S1063454123020140