Helmholtz decomposition theorem and Blumenthal's extension by regularization

• Published in: Condensed Matter Physics
• Date: 2017
• Main Authors: Petrascheck, D., Folk, R.
• Format: Article
• Language: English
• Published: Інститут фізики конденсованих систем НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/156568
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Helmholtz decomposition theorem and Blumenthal's extension by regularization / D. Petrascheck, R. Folk // Condensed Matter Physics. — 2017. — Т. 20, № 1. — С. 13002: 1–11. — Бібліогр.: 22 назв. — англ.

Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is possible for any asymptotically weakly decreasing vector field. He used a regularization method in...