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

The aim of this paper is to prove ${\mathrm{\Gamma }}^{1,\alpha }$ 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].