Calculus of Variations and Geometric Measure Theory

D. Lučić - E. Pasqualetto - T. Rajala

Characterisation of upper gradients on the weighted Euclidean space and applications

created by lučić on 24 Jul 2020



Inserted: 24 jul 2020

Year: 2020

ArXiv: 2007.11904 PDF


In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz functions.