Search

We study the asymptotic behaviour of a p-harmonic measure ?p, p 2 (1,8], in a domain - O R2, subject to certain regularity constraints. Our main result is that ?p(B(w, d) ∩ ?O , w0) dq as d → 0+ 1/2 ± q as ± ! 0+, where q = q(v; p) is given explicitly as a function of v and p. Here, v is related to properties of - near w. If p = 8, this extends to some domains in Rn. By a result due to Hirata, our result implies that the p-Green function for p 2 (1; 2) is not quasi-symmetric in plane C1,1-domains. [ABSTRACT FROM AUTHOR]

In this paper we prove a boundary Harnack inequality for positive functions which vanish continuously on a portion of the boundary of a bounded domain-Ω R2 and which are solutions to a general equation of p-Laplace type, 1 < p < ∞. We also establish the same type of result for solutions to the Aronsson type equation ∇(F(x,∇u)) . Fη(x,∇u) = 0. Concerning Ωwe only assume that ∂Ω is a quasicircle. In particular, our results generalize the boundary Harnack inequalities in [BL] and [LN2] to operators with variable coefficients. [ABSTRACT FROM AUTHOR]