English

Characterisation of upper gradients on the weighted Euclidean space and applications

Functional Analysis 2020-07-24 v1 Analysis of PDEs

Abstract

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.

Keywords

Cite

@article{arxiv.2007.11904,
  title  = {Characterisation of upper gradients on the weighted Euclidean space and applications},
  author = {Danka Lučić and Enrico Pasqualetto and Tapio Rajala},
  journal= {arXiv preprint arXiv:2007.11904},
  year   = {2020}
}

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39 pages