6 papers · 1 filter
Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality
Bao Yu, Yang Zhou
Let and . We first prove the local trace analogue of the sharp one-bubble critical-point stability theorem of Liu and Zhang~\cite{LiuZhang2025}: near a positive trac…
Liouville theorem for subcritical nonlinear heat equation
Yang Zhou
We obtain a Li-Yau-type estimate for nonnegative ancient solutions to the subcritical semilinear heat equation $\frac{\p u}{\p t}=\De u+u^p$ in $\rz^n\times(-\infty,0)$. Then, we c…
Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary
Jingbo Dou, Yazhou Han, Shuang Yuan +1
In this paper, we establish a sharp Onofri trace inequality on the upper half space by considering the limiting case of Sobolev trace inequalit…
Liouville type theorem for a class of quasilinear p-Laplace type equations in the half space
Bao Yu, Yang Zhou
We use the method of vector fields to obtain a Liouville-type theorem for a class of quasilinear p-Laplace type equations with conormal boundary condition in the half space. These…
A priori estimates for parabolic Monge-Ampère type equations
Yang Zhou, Ruixuan Zhu
We prove the existence and regularity of convex solutions to the first initial-boundary value problem for the parabolic Monge-Ampère equationn $$ \left\{\begin{eqnarray} &&-u_t+\d…
Global regularity for Monge-Ampère equations on planar convex domains
Qing Han, Jiakun Liu, Yang Zhou
In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation on strictly convex but not uni…