Characterisation of upper gradients on the weighted Euclidean space and applications
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.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202103222043Use this for linking
Review status
Peer reviewed
ISSN
0373-3114
DOI
https://doi.org/10.1007/s10231-021-01088-4
Language
English
Published in
Annali di Matematica Pura ed Applicata
Citation
- Lučić, D., Pasqualetto, E., & Rajala, T. (2021). Characterisation of upper gradients on the weighted Euclidean space and applications. Annali di Matematica Pura ed Applicata, 200(6), 2473-2513. https://doi.org/10.1007/s10231-021-01088-4
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
All authors are partially supported by the Academy of Finland, Project 314789.
Copyright© 2021 the Authors