$ε$-Approximability and Quantitative Fatou Property on Lipschitz-graph domains for a class of non-harmonic functions
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| Format: | Preprint |
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2024
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| _version_ | 1866913615966109696 |
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| author | Adamowicz, Tomasz González, María J. Gryszówka, Marcin |
| author_facet | Adamowicz, Tomasz González, María J. Gryszówka, Marcin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_13072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $ε$-Approximability and Quantitative Fatou Property on Lipschitz-graph domains for a class of non-harmonic functions Adamowicz, Tomasz González, María J. Gryszówka, Marcin Analysis of PDEs Complex Variables (Primary) 42B37, (Secondary) 31B25, 42B25 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. |
| title | $ε$-Approximability and Quantitative Fatou Property on Lipschitz-graph domains for a class of non-harmonic functions |
| topic | Analysis of PDEs Complex Variables (Primary) 42B37, (Secondary) 31B25, 42B25 |
| url | https://arxiv.org/abs/2412.13072 |