DIFFERENTIABILITY OF MAPPINGS OF THE SOBOLEV SPACE $W^1_{n−1}$ WITH CONDITIONS ON THE DISTORTION FUNCTION Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2018, Volume: 59, Number: 6, Pages: 983–1005 Pages count : 23 DOI: 10.1134/S0037446618060034 | ||||
| Tags | quasiconformal analysis, Sobolev space, capacity estimate, differentiability, Liouville theorem | ||||
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Abstract:
We define two scales of the mappings that depend on two real parameters p and q, with
n−1 ≤ q ≤ p < ∞, as well as a weight function θ. The case q = p = n and θ ≡ 1 yields the well-known
mappings with bounded distortion. The mappings of a two-index scale are applied to solve a series of
problems of global analysis and applications. The main result of the article is the a.e. differentiability
of mappings of two-index scales.
Cite:
Vodopyanov S.K.
DIFFERENTIABILITY OF MAPPINGS OF THE SOBOLEV SPACE $W^1_{n−1}$ WITH CONDITIONS ON THE DISTORTION FUNCTION
Siberian Mathematical Journal. 2018. V.59. N6. P.983–1005. DOI: 10.1134/S0037446618060034 WOS Scopus OpenAlex
DIFFERENTIABILITY OF MAPPINGS OF THE SOBOLEV SPACE $W^1_{n−1}$ WITH CONDITIONS ON THE DISTORTION FUNCTION
Siberian Mathematical Journal. 2018. V.59. N6. P.983–1005. DOI: 10.1134/S0037446618060034 WOS Scopus OpenAlex
Original:
Водопьянов С.К.
О дифференцируемости отображений класса Соболева $W^1_{n-1}$ с некоторыми условиями на функцию искажения
Сибирский математический журнал. 2018. Т.59. №6. С.983-1005. DOI: 10.17377/smzh.2018.59.60
О дифференцируемости отображений класса Соболева $W^1_{n-1}$ с некоторыми условиями на функцию искажения
Сибирский математический журнал. 2018. Т.59. №6. С.983-1005. DOI: 10.17377/smzh.2018.59.60
Dates:
| Submitted: | Jul 11, 2018 |
Identifiers:
| Web of science: | WOS:000454441000003 |
| Scopus: | 2-s2.0-85057482206 |
| OpenAlex: | W2906333871 |