Expansion of harmonic functions near the boundary of Dini domains

2021/07/13 by Carlos E. Kenig, Kenig, Carlos, Zihui Zhao +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2107.06324

openalex publication_date 2021/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let u be a harmonic function in a C¹-Dini domain, such that u vanishes on an open set of the boundary. We show that near every point in the open set, u can be written uniquely as the sum of a non-trivial homogeneous harmonic polynomial and an error term of higher degree (depending on the Dini parameter). In particular, this implies that u has a unique tangent function at every such point, and that the convergence rate to the tangent function can be estimated. We also study the relationship of tangent functions at nearby points in a special case.

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