Regularity for critical points of convex functionals on Hessian spaces

Arunima Bhattacharya

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arXiv · 2108.01319

Regularity for critical points of convex functionals on Hessian spaces

Arunima Bhattacharya

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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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Arunima Bhattacharya. 2021-08-03. Regularity for critical points of convex functionals on Hessian spaces. https://arxiv.org/abs/2108.01319

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