Calculus of Variations and Geometric Measure Theory

E. Pasqualetto

A short proof of the existence of master test plans

created by pasqualetto on 08 Mar 2022
modified on 30 Sep 2022


Accepted Paper

Inserted: 8 mar 2022
Last Updated: 30 sep 2022

Journal: Archiv der Mathematik
Year: 2022

ArXiv: 2203.02736 PDF


The aim of this brief note is to provide a quick and elementary proof of the following known fact: on a metric measure space whose Sobolev space is separable, there exists a test plan that is sufficient to identify the minimal weak upper gradient of every Sobolev function.