论文标题
抛物线$ k $ -Hessian方程的衍生物和Liouville类型定理的内部估计值
Interior estimates of derivatives and a Liouville type theorem for Parabolic $k$-Hessian equations
论文作者
论文摘要
在本文中，我们建立了$ k $ -convex-Monotone解决方案的梯度和pogorelov估计，以寄生在抛物线$-U_Tσ_K（λ（d^2U））=ψ（x，x，t，u）$。我们还应用此类估计值获得了Liouville类型的结果，该结果指出，任何$ K $ -CONVEX-蒙托酮和$ C^{4,2} $ u $ to $ u $ to $-u_tσ_k（λ（d^2u））= 1 $ in $ \ \ \ \ \ \ m athbb {r} $ x $，根据$ u $的某些增长假设。
In this paper, we establish the gradient and Pogorelov estimates for $k$-convex-monotone solutions to parabolic $k$-Hessian equations of the form $-u_tσ_k(λ(D^2u))=ψ(x,t,u)$. We also apply such estimates to obtain a Liouville type result, which states that any $k$-convex-monotone and $C^{4,2}$ solution $u$ to $-u_tσ_k(λ(D^2u))=1$ in $\mathbb{R}^n\times(-\infty,0]$ must be a linear function of $t$ plus a quadratic polynomial of $x$, under some growth assumptions on $u$.
