Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - S. Nicolussi Golo - F. Serra Cassano

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.


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