Removable singularities for bounded A-(super)harmonic and quasi(super)harmonic functions on weighted Rn. (September 2022) - Björn, Anders
Abstract: It is well known that sets of p -capacity zero are removable for bounded p -harmonic functions, but on metric spaces there are examples of removable sets of positive capacity. In this paper, we show that this can happen even on unweighted R n when n > p, although only in very special cases. A complete characterization of removable singularities for bounded A -harmonic functions on weighted R n, n ≥ 1, is also given, where the weight is p -admissible. The same characterization is also shown to hold for bounded quasiharmonic functions on weighted R n, n ≥ 2, as well as on unweighted R . For bounded A -superharmonic functions and bounded quasisuperharmonic functions on weighted R n, n ≥ 2, we show that relatively closed sets are removable if and only if they have zero capacity.