Modulus of continuity and Martin boundary of a cylinder and a cone for p-harmonic functions
翼 伊藤 · Institutional Repositories DataBase (IRDB) · 2014
Let 1 < p < ∞ and let X be a metric measure space with a doubling measure and a (1, p)-Poincaré inequality.Let Ω be a bounded domain in X.For a function f on ∂Ω we denote by P Ω f the p-Dirichlet solution of f over Ω.It is well known that if Ω is p-regular and f ∈ C(∂Ω), then P Ω f is p-harmonic in Ω and continuous in Ω.We characterize the family of domains Ω such that improved continuity of boundary functions f ensures improved continuity of P Ω f .We specify such improved continuity if X is Ahlfors regular and X \ Ω is uniformly p-fat.