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arXiv · 2311.03481

$\mathbf{C^2}$-Lusin approximation of strongly convex functions

Daniel Azagra·Marjorie Drake·Piotr Hajłasz
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Abstract

We prove that if $u:\mathbb{R}^n\to\mathbb{R}$ is strongly convex, then for every $\varepsilon>0$ there is a strongly convex function $v\in C^2(\mathbb{R}^n)$ such that $|\{u\neq v\}|<\varepsilon$ and $\Vert u-v\Vert_\infty<\varepsilon$.

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Daniel Azagra, Marjorie Drake, Piotr Hajłasz. 2023-11-06. $\mathbf{C^2}$-Lusin approximation of strongly convex functions. https://arxiv.org/abs/2311.03481

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