Expansion of harmonic functions near the boundary of Dini domains

• Carlos Kenig ^[1] ; Zihui Zhao ^[1]
  1. [1] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº Extra 7, 2022 (Ejemplar dedicado a: Special issue in honor of Antonio Córdoba and José Luis Fernández), págs. 2117-2152
• Idioma: inglés
• DOI: 10.4171/RMI/1380
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• Resumen

  • Let u be a harmonic function in a 1C1-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