Expansion of harmonic functions near the boundary of Dini domains

نویسندگان

چکیده

Let $u$ be a harmonic function in $C^1$-Dini domain such that vanishes on an open set of the boundary. We show near every point set, can written uniquely as sum non-trivial homogeneous polynomial and error term higher degree (depending Dini parameter). In particular, this implies has unique tangent at point, convergence rate to estimated. also study relationship functions nearby points special case.

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ژورنال

عنوان ژورنال: Revista Matematica Iberoamericana

سال: 2022

ISSN: ['2235-0616', '0213-2230']

DOI: https://doi.org/10.4171/rmi/1380