A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$
Functional Analysis
2025-02-05 v1
Abstract
We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space as the difference of two non-negative functions in the same space with control of their norms.
Cite
@article{arxiv.1807.05221,
title = {A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$},
author = {Augusto C. Ponce and Daniel Spector},
journal= {arXiv preprint arXiv:1807.05221},
year = {2025}
}