标题： Hessian空间上凸泛函的临界点的正则性 显示英文标题

标题： Regularity for critical points of convex functionals on Hessian spaces

摘要： 我们考虑形式为$\int F(D^2u)$的变分积分，其中$F$在 Hessian 空间上是凸的且光滑。 我们证明，如果$u$的 Hessian 具有小振荡，则在紧支撑变化下该泛函的临界点$u\in W^{2,\infty}$是光滑的。 显示英文摘要

摘要： We consider variational integrals of the form $\int F(D^2u)$ where $F$ is convex and smooth on the Hessian space. We show that a critical point $u\in W^{2,\infty}$ of such a functional under compactly supported variations is smooth if the Hessian of $u$ has a small oscillation.