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

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