The Gauss-Green theorem for bounded vector fields with divergence measure on sets of finite perimeter

0570780 - MÚ 2024 RIV US eng J - Journal Article
Šilhavý, Miroslav
The Gauss-Green theorem for bounded vector fields with divergence measure on sets of finite perimeter.
Indiana University Mathematics Journal. Roč. 72, č. 1 (2023), s. 29-42. ISSN 0022-2518. E-ISSN 1943-5258
Institutional support: RVO:67985840
Keywords : divergence measure fields * generalized Gauss-Green theorems * normal traces * sets of finite perimeter
OECD category: Applied mathematics
Impact factor: 1.1, year: 2022
Method of publishing: Limited access
https://dx.doi.org/10.1512/iumj.2023.72.9407

A bounded divergence measure field is a bounded measurable function q = (q1, . . ., qn) on Rn whose weak divergence is a finite signed measure. The Gauss-Green theorem for this class of fields on sets of finite perimeter was established independently by Chen & Torres and the present author in 2005. To emphasize the essentially simple nature of this result, the original proof is here outlined, with some amendments. In addition, future developments are briefly recapitulated together with some remarks on the later proof by Chen, Torres, & Ziemer.
Permanent Link: https://hdl.handle.net/11104/0342121