@article{94972d2aafad41c9ac49b0cf6fc4005e,
title = "A decomposition by non-negative functions in the Sobolev Space Wk,1 ",
abstract = "We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space Wk,1(ℝd) as the difference of two non-negative functions in the same space with control of their norms.",
author = "Ponce, {Augusto C.} and Daniel Spector",
note = "Funding Information: Acknowledgements. This work was initiated while the first author was visiting the Department of Applied Mathematics of the National Chiao Tung University with support from the National Center for Theoretical Sciences, Wallonie-Bruxelles International, and the Fonds de la Recherche scientifique (grant no. J.0020.18). He warmly thanks the Department for the invitation and hospitality. The second author is supported by the Taiwan Ministry of Science and Technology (grant nos. 105-2115-M-009-004-MY2 and 107-2918-I-009-003). Publisher Copyright: {\textcopyright} 2020 Department of Mathematics, Indiana University. All rights reserved.",
year = "2020",
doi = "10.1512/iumj.2020.69.8237",
language = "English",
volume = "69",
pages = "151--169",
journal = "Indiana University Mathematics Journal",
issn = "0022-2518",
publisher = "Indiana University",
number = "1",
}