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- W4313447518 abstract "In this paper we prove that any very weak $s$-harmonic function $u$ in the unit ball $B$ is locally weakly $s$-harmonic. First, via localisation and bootstrap methods we prove that $u$ gains more summability. Then we prove $H^s$ Sobolev regularity using a generalisation of the Nirenberg differential quotients method to the nonlocal setting that allows to get rid of the singularity of the integral kernel. Finally, $L^2$ estimates lead us to $H^{2s}$ Sobolev regularity." @default.
- W4313447518 created "2023-01-06" @default.
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- W4313447518 date "2022-12-30" @default.
- W4313447518 modified "2023-10-18" @default.
- W4313447518 title "Local Regularity of very weak $s$-harmonic functions" @default.
- W4313447518 doi "https://doi.org/10.48550/arxiv.2212.14757" @default.
- W4313447518 hasPublicationYear "2022" @default.
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