A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related To Hörmander's Vector Fields

. In this paper, we consider the divergence degenerate elliptic equation with bounded coefﬁcients constructed by H¨ormander’s vector ﬁelds. We prove a De Giorgi type result, i.e., the local H¨older continuity for the weak solutions to the equation by providing a De Giorgi type lemma and extending the Moser iteration to the setting here. As a consequence, the Harnack inequality of weak solutions is also given