Free boundary problems in the spirit of Sakai’s theorem

نویسندگان

چکیده

A Schwarz function on an open domain Ω is a holomorphic satisfying S(ζ)=ζ ¯ Γ, which part of the boundary Ω. Sakai in 1991 gave complete characterization admitting function. In fact, if simply connected and Γ=∂Ω∩D(ζ 0 ,r), then Γ has to be regular real analytic (with possible cusps). Sakai’s result natural applications 1) quadrature domains, 2) free problem for Δu=1 equation. our scenarios can be, respectively, from real-analytic just C ∞ , except harmonic-measure-zero set, or finitely many points.

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ژورنال

عنوان ژورنال: Comptes Rendus Mathematique

سال: 2022

ISSN: ['1631-073X', '1778-3569']

DOI: https://doi.org/10.5802/crmath.259