2018/10/04 by Eric Schippers, Wolfgang Staubach, Schippers, Eric +1
Computer Science · Mathematics · #30C62 #30F15 #58J05 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1810.02147
openalex publication_date 2018/10/04 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
Let R be a compact surface and let \Γ be a Jordan curve which\nseparates R into two connected components \Σ1 and \Σ2. A\nharmonic function h1 on \Σ1 of bounded Dirichlet norm has boundary\nvalues H in a certain conformally invariant non-tangential sense on \Γ.\nWe show that if \Γ is a quasicircle, then there is a unique harmonic\nfunction h2 of bounded Dirichlet norm on \Σ2 whose boundary values\nagree with those of h1. Furthermore, the resulting map from the Dirichlet\nspace of \Σ1 into \Σ2 is bounded with respect to the Dirichlet\nsemi-norm.\n