Semiregular and strongly irregular boundary points for p-harmonic functions on unbounded sets in metric spaces

The trichotomy between regular, semiregular, and strongly irregular boundary points for p-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincare inequality, 1 < p < infinity. We show that these are local properties. We also deduce several characterizations of semiregular points and strongly irregular points. In particular, semiregular points are characterized by means of capacity, p-harmonic measures, removability, and semibarriers.Funding Agencies|Swedish Research CouncilSwedish Research CouncilEuropean Commission [2016-03424]