Year: 2011
Type: preprint
Abstract: It is shown that an arbitrary function from $D\subset \R^n$ to $\R^m$ will become $C^{0,α}$-continuous in almost every $x\in D$ after restriction to a certain subset with limit point $x$. For $n\geq m$ differentiability can be obtained. Examples show the Hölder exponent $α=\min\{1,\frac{n}{m}\}$ is optimal.
Source: arXiv (Cornell University)
Author: Elling, Volker
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2164637784