Abstract
This paper is the first part of a program aimed at studying the regularity of sub-elliptic free boundaries. In the setting of Carnot groups we establish the optimal interior regularity of the solution to the obstacle problem in terms of the Folland-Stein non-isotropic class Γ 1,1 . This result constitutes the sub-elliptic counterpart of the classical C 1,1 regularity for Laplace equation. We also prove non-degeneracy properties of the solution and of its free boundary.
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