$\mathbf{C^2}$-Lusin approximation of strongly convex functions (2311.03481v2)

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 $\Vert u-v\Vert_\infty<\varepsilon$.