TY - JOUR
T1 - Liouville Type Theorems for a Class of General Parabolic Hessian Quotient Type Equations
AU - Liu , Hui
AU - Xiang , Ni
AU - Zheng , Lina
JO - Analysis in Theory and Applications
VL - 3
SP - 238
EP - 258
PY - 2025
DA - 2025/09
SN - 41
DO - http://doi.org/10.4208/ata.OA-2025-0006
UR - https://global-sci.org/intro/article_detail/ata/24485.html
KW - Parabolic $(k,l)$-Hessian quotient type equations, Pogorelov type estimates, Liouville type theorems.
AB - <p style="text-align: justify;">We first consider the a priori estimates to a class of general parabolic $(k,l)-$ Hessian quotient type equations of the form<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20250929/1759128074702651.png" title="1759128074702651.png" alt="36cca9c7cc11a690f7a735685385904.png" width="431" height="64"/></p><p style="text-align: justify;">with $0{\le}1&lt;k{\le}n.$ We&nbsp;derive that any $k-$admissible-monotone solution to<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20250929/1759128245727798.png" title="1759128245727798.png" alt="7272fa253479ab71a9656a5110b7a9c.png" width="399" height="64"/></p><p style="text-align: justify;">or<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20250929/1759128272869592.png" title="1759128272869592.png" alt="7cde00a4f7b91e282a13e73df98782e.png" width="364" height="50"/></p><p style="text-align: justify;">has interior gradient estimates and Pogorelov type estimates. As an application, we
 prove Liouville type theorems for these equations.<br/></p>