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ɛ-approximability and quantitative Fatou property on Lipschitz-graph domains for a class of non-harmonic functions
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 31 March 2026, pp. 1-37
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We study the class of functions on Lipschitz-graph domains satisfying a differential-oscillation condition and show that such functions are
$\varepsilon$-approximable. As a consequence, we obtain the quantitative Fatou theorem in the spirit of works, for example, by Garnett [6] and Bortz–Hofmann [1]. Such a class contains harmonic functions, as well as non-harmonic ones, for example, nonnegative subharmonic functions whose gradient norm is quasi-nearly subharmonic, as illustrated by our discussion.
