$\mathbf{C^2}$-Lusin approximation of strongly convex functions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911811136126976 |
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| author | Azagra, Daniel Drake, Marjorie Hajłasz, Piotr |
| author_facet | Azagra, Daniel Drake, Marjorie Hajłasz, Piotr |
| contents | 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 $\Vert u-v\Vert_\infty<\varepsilon$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03481 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $\mathbf{C^2}$-Lusin approximation of strongly convex functions Azagra, Daniel Drake, Marjorie Hajłasz, Piotr Classical Analysis and ODEs Primary 26B25, Secondary 41A29, 52A20, 52A27 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 $\Vert u-v\Vert_\infty<\varepsilon$. |
| title | $\mathbf{C^2}$-Lusin approximation of strongly convex functions |
| topic | Classical Analysis and ODEs Primary 26B25, Secondary 41A29, 52A20, 52A27 |
| url | https://arxiv.org/abs/2311.03481 |