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arXiv · 2412.13072

$\epsilon$-Approximability and Quantitative Fatou Property on Lipschitz-graph domains for a class of non-harmonic functions

Tomasz Adamowicz·María J. González·Marcin Gryszówka
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Abstract

We study the class of functions on Lipschitz-graph domains satisfying a differential-oscillation condition and show that such functions are $\epsilon$-approximable. As a consequence we obtain the quantitative Fatou theorem in the spirit of works e.g. by Garnett and Bortz-Hofmann. Such a class contains harmonic functions, as well as non-harmonic ones, for example nonnegative subharmonic functions, as illustrated by our discussion.

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Tomasz Adamowicz, María J. González, Marcin Gryszówka. 2024-12-17. $\epsilon$-Approximability and Quantitative Fatou Property on Lipschitz-graph domains for a class of non-harmonic functions. https://arxiv.org/abs/2412.13072

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