Compactness methods for ${\Gamma }^{1,\alpha }$ boundary Schauder estimates in Carnot groups

Abstract

The aim of this paper is to prove ${\Gamma }^{1,\alpha }$ Schauder estimates near a $C^{1,\alpha }$ non-characteristic portion of the boundary for ${\Gamma }^{0,\alpha }$ perturbations of horizontal Laplaceans in Carnot groups. This situation of minimally smooth domains presents itself naturally in the study of subelliptic free boundary problems of obstacle type, see [15].

revision of the previous version with a few updated references