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 - <p style="text-align: justify;">In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander&#39;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.</p>