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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02798 |
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Table of Contents:
- Given a porous compact $K \subset \mathbb{R}^d$ and a continuity modulus $ω$, we prove a quantitative Jackson-Bernstein type theorem on harmonic approximation. That is, a function $f$ belongs to the class $\mathrm{Lip}_ω(K)$ if and only if $f$ can be approximated uniformly on $K$ with a rate of $ω(δ)$ by a function that is harmonic in the $δ$-neighborhood of $K$, provided the uniform estimate $ω(δ)/δ$ on the gradient holds.