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Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results

Grigori Rozenblum, Nikolai Shirokov

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Source: Crossref

Published: Apr 6, 2026

DOI: 10.1007/s11856-026-2906-7

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Source abstract

Abstract We establish that a generalized Hölder continuous function on an ( m − 2)-Ahlfors regular compact set in ℝ m can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function.

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Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results — Mathematical Frontier Network