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math.AP2023
Interior derivative estimates and Bernstein theorem for Hessian quotient equations
Limei Dai, Jiguang Bao, Bo Wang
In this paper, we obtain the interior derivative estimates of solutions for elliptic and parabolic Hessian quotient equations. Then we establish the Bernstein theorem for parabolic…
math.AP2023
Entire solutions to the parabolic Monge--Ampère equation with unbounded nonlinear growth in time
Ning An, Jiguang Bao, Zixiao Liu
The Liouville type theorem on the parabolic Monge--Ampère equation states that any entire parabolically convex classical solution must be of form up…
math.AP2023
Existence of entire solutions to the Lagrangian mean curvature equations in supercritical phase
Zixiao Liu, Cong Wang, Jiguang Bao
In this paper, we establish the existence and uniqueness theorem of entire solutions to the Lagrangian mean curvature equations with prescribed asymptotic behavior at infinity. The…