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

Abstract

The trichotomy between regular, semiregular, and strongly irregular boundary points for $$p$$ p -harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $$p$$ p -Poincaré inequality, $$1<p<\infty $$ 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, $$p$$ p -harmonic measures, removability, and semibarriers.