Abstract
AbstractThe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics
Reference28 articles.
1. Adamowicz, T., Björn, A., Björn, J.: Regularity of $$p(\cdot )$$-superharmonic functions, the Kellogg property and semiregular boundary points. Ann. Inst. H. Poincaré Anal. Non Linéaire 31, 1131–1153 (2014)
2. Björn, A.: Characterizations of $$p$$-superharmonic functions on metric spaces. Stud. Math. 169, 45–62 (2005)
3. Björn, A.: Removable singularities for bounded $$p$$-harmonic and quasi(super)harmonic functions on metric spaces. Ann. Acad. Sci. Fenn. Math. 31, 71–95 (2006)
4. Björn, A.: A regularity classification of boundary points for $$p$$-harmonic functions and quasiminimizers. J. Math. Anal. Appl. 338, 39–47 (2008)
5. Björn, A., Björn, J.: Boundary regularity for $$p$$-harmonic functions and solutions of the obstacle problem on metric spaces. J. Math. Soc. Jpn. 58, 1211–1232 (2006)