p$$ -Harmonic functions in the Heisenberg group: boundary behaviour in domains well-approximated by non-characteristic hyperplanes

n this paper we study, for given p, 1 < p < 8, the boundary behaviour of non-negative p-harmonic functions in the Heisenberg group H-n, i.e., we consider weak solutions tothe non-linear and potentially degenerate partial differential equation Sigma (2n)(i=1) Xi (vertical bar Xu vertical bar(p-2) X(i)u) = 0 where the vector fields X1, ... , X-2n form a basis for the space of left-invariant vector fields on Hn. In particular, we introduce a set of domains Omega subset of H-n which we refer to asdomains well-approximated by non-characteristic hyperplanes and in Omega we prove, for 2 <= p < infinity, the boundary Harnack inequality as well as the Holder continuity for ratios of positive p-harmonic functions vanishing on a portion of partial derivative Omega