A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related to Hörmander's Vector Fields
Lingling Hou · Journal of Partial Differential Equations · 2022
In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander's vector fields. We prove a De Giorgi type result, i.e., the local Hölder 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.