Semialgebraic Calderon-Zygmund theorem on regularization of the distance function
| Autor: | Kocel-Cynk, Beata, Pawłucki, Wiesław, Valette, Anna |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Mathematische Annalen (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00208-023-02795-4 |
| Popis: | We prove that, for any closed semialgebraic subset $W$ of $\mathbb{R}^n$ and for any positive integer $p$, there exists a Nash function $f:\mathbb{R}^n\setminus W\longrightarrow (0, \infty)$ which is equivalent to the distance function from $W$ and at the same time it is $\Lambda_p$-regular in the sense that $|D^\alpha f(x)|\leq C d(x, W)^{1- |\alpha|}$, for each $x\in \mathbb{R}^n\setminus W$ and each $\alpha\in \mathbb{N}^n$ such that $1\leq |\alpha|\leq p$, where $C$ is a positive constant. In particular, $f$ is Lipschitz. Some applications of this result are given. Comment: Final version |
| Databáze: | arXiv |
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