Обобщение одной леммы Е. А. Полецкого на классы пространственных отображений
Zhytomyr State University Library
View Archive Info| Field | Value | |
| Relation |
http://eprints.zu.edu.ua/13845/
|
|
| Title |
Обобщение одной леммы Е. А. Полецкого на классы пространственных отображений
|
|
| Creator |
Севастьянов, Є. О.
|
|
| Subject |
Mathematical Analysis
|
|
| Description |
The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings f ∈ W1,n loc such that their outer dilatation KO(x, f) belongs to Ln−1 loc and the measure of the set Bf of branching points of f is equal to zero have finite length distortion. In other words, the images of almost all curves γ in the domain D under the considered mappings f : D → Rn, n ≥ 2, are locally rectifiable, f possesses the (N)-property with respect to length on γ , and, furthermore, the (N)-property also holds in the inverse direction for liftings of curves. The results obtained generalize the well-known Poletskii lemma proved for quasiregular mappings. |
|
| Publisher |
Національна академія наук
|
|
| Date |
2009
|
|
| Type |
Article
PeerReviewed |
|
| Format |
text
|
|
| Language |
uk
russian |
|
| Identifier |
http://eprints.zu.edu.ua/13845/1/1.5.pdf
Севастьянов, Є. О. (2009) Обобщение одной леммы Е. А. Полецкого на классы пространственных отображений. Український математичний журнал, 61 (7). pp. 969-975. ISSN 1027-3190 |
|