| Abstract : In this talk we discuss the Martin boundary problem for p harmonic functions (for p in (1,∞)) in Reifenberg flat domains and the corresponding question of when a minimal positive p harmonic function (with respect to a given boundary point) is unique up to constant multiples. Proofs use recent boundary Harnack inequalities of Lewis and Nystršom for the ratio of two positive p harmonic functions vanishing on a portion of the boundary of a Reifenberg flat domain. So these inequalities will also be discussed. In particular we outline a proof that shows the p Martin boundary can be identified with the topological boundary in sufficiently flat domains (e.g., C1 domains). |