2024/12/17 by Tomasz Adamowicz, Adamowicz, Tomasz, María José González +3
Computer Science · Mathematics · #(Primary) 42B37 #(Secondary) 31B25 #42B25 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2412.13072
openalex publication_date 2024/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the class of functions on Lipschitz-graph domains satisfying a differential-oscillation condition and show that such functions are ε-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.