# Optimal $C^\infty$-approximation of functions with exponentially or sub-exponentially integrable derivative

created by nicolussigolo on 08 Mar 2022
modified on 02 Aug 2022

[BibTeX]

preprint

Inserted: 8 mar 2022
Last Updated: 2 aug 2022

Year: 2022

ArXiv: 2203.03306 PDF

Abstract:

We discuss Meyers-Serrin's type results for smooth approximations of functions $b=b(t,x):\mathbb{R}\times\mathbb{R}^n\to\mathbb{R}^m$, with convergence of an energy of the form $\int_{\mathbb{R}}\int_{\mathbb{R}^n} w(t,x) \varphi\left( Db(t,x) \right)\mathrm{d} x \mathrm{d} t\,,$ where $w>0$ is a suitable weight function, and $\varphi:[0,\infty)\to [0,\infty)$ is a convex function with $\varphi(0)=0$ having exponential or sub-exponential growth.