Decay of a p-harmonic measure in the plane
Niklas L. P. Lundström, Jonatan Vasilis · Annales Academiae Scientiarum Fennicae Mathematica · 2013
We study the asymptotic behaviour of a p-harmonic measure ω p , p ∈ (1, ∞], in a domain Ω ⊆ R 2 , subject to certain regularity constraints.Our main result is that ω p B(w, δ) ∩ ∂Ω, w 0 ≈ δ q as δ → 0 + , where q = q(v, p) is given explicitly as a function of v and p.Here, v is related to properties of Ω near w.If p = ∞, this extends to some domains in R n .By a result due to Hirata, our result implies that the p-Green function for p ∈ (1, 2) is not quasi-symmetric in plane C 1,1 -domains.