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 -Poincaré inequality, 1 < p < ∞ . 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. [ABSTRACT FROM AUTHOR]