Regularity for critical points of convex functionals on Hessian spaces

Bhattacharya, Arunima

doi:10.1090/proc/16051

Regularity for critical points of convex functionals on Hessian spaces
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Proc. Amer. Math. Soc. 150 (2022), 5217-5230 Request permission

Abstract:

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.

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