Dimension estimate for the two-sided points of planar Sobolev extension domains

Abstract

In this paper we give an estimate for the Hausdorff dimension of the set of two-sided points of the boundary of bounded simply connected Sobolev W1,p-extension domain for 1 < p < 2. Sharpness of the estimate is shown by examples. We also prove the equivalence of different definitions of two-sided points.