Helmholtz decomposition theorem and Blumenthal's extension by regularization
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...
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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2017
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| Series: | Condensed Matter Physics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/156568 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 his proof which can be
extended to prove the theorem even for vector fields asymptotically increasing sublinearly. Blumenthal’s result
is then applied to the time-dependent fields of the dipole radiation and an artificial sublinearly increasing field. |
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