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

Anders Björn, Daniel Hansevi

• 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-Poincaré inequality. 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.