TY - JOUR T1 - A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related to Hörmander's Vector Fields AU - Hou , Lingling JO - Journal of Partial Differential Equations VL - 1 SP - 22 EP - 47 PY - 2022 DA - 2022/12 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n1.2 UR - https://global-sci.org/intro/article_detail/jpde/21291.html KW - Divergence degenerate elliptic equation KW - Hörmander's vector fields KW - De Giorgi type result KW - Harnack inequality. AB -

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.