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.
The author's research was supported in Section 2 by the Ministry of Science and Education of the Russian Federation (Grant 1.3087.2017/4.6) and in Sections 3 and 4 by the Russian Foundation for Basic Research (Grant 17-01-00801).
Citation:
S. K. Vodopyanov, “Differentiability of mappings of the Sobolev space W1n−1 with conditions on the distortion function”, Sibirsk. Mat. Zh., 59:6 (2018), 1240–1267; Siberian Math. J., 59:6 (2018), 983–1005
\Bibitem{Vod18}
\by S.~K.~Vodopyanov
\paper Differentiability of mappings of the Sobolev space $W^1_{n-1}$ with conditions on the distortion function
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 6
\pages 1240--1267
\mathnet{http://mi.mathnet.ru/smj3041}
\crossref{https://doi.org/10.17377/smzh.2018.59.603}
\elib{https://elibrary.ru/item.asp?id=38644835}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 6
\pages 983--1005
\crossref{https://doi.org/10.1134/S0037446618060034}
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Linking options:
https://www.mathnet.ru/eng/smj3041
https://www.mathnet.ru/eng/smj/v59/i6/p1240
This publication is cited in the following 12 articles:
Izv. Math., 87:4 (2023), 683–725
S. K. Vodopyanov, “Coincidence of set functions in quasiconformal analysis”, Sb. Math., 213:9 (2022), 1157–1186
S. K. Vodopyanov, N. A. Evseev, “Functional and analytical properties of a class of mappings of quasiconformal analysis on Carnot groups”, Siberian Math. J., 63:2 (2022), 233–261
S. K. Vodopyanov, “On Poletsky-type modulus inequalities for some classes of mappings”, Vladikavk. matem. zhurn., 24:4 (2022), 58–69
S. K. Vodopyanov, “TWO-WEIGHTED COMPOSITION OPERATORS ON SOBOLEV SPACES AND QUASICONFORMAL ANALYSIS”, J Math Sci, 266:3 (2022), 491
S. K. Vodopyanov, “Moduli inequalities for W1n−1,loc-mappings with weighted bounded (q,p)-distortion”, Complex Var. Elliptic Equ., 66:6-7, SI (2021), 1037–1072
S. K. Vodopyanov, A. O. Tomilov, “Functional and analytic properties of a class of mappings in quasi-conformal analysis”, Izv. Math., 85:5 (2021), 883–931
S. K. Vodopyanov, “On the equivalence of two approaches to problems of quasiconformal analysis”, Siberian Math. J., 62:6 (2021), 1010–1025
S. K. Vodopyanov, “The regularity of inverses to Sobolev mappings and the theory of Qq,p-homeomorphisms”, Siberian Math. J., 61:6 (2020), 1002–1038
Ruslan Salimov, Mariia Stefanchuk, “On the local properties of solutions of the nonlinear Beltrami equation”, UMB, 17:1 (2020), 77
A. Molchanova, S. Vodopyanov, “Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity”, Calc. Var. Partial Differ. Equ., 59:1 (2019), 17
S. K. Vodopyanov, “Basics of the quasiconformal analysis of a two-index scale of spatial mappings”, Siberian Math. J., 59:5 (2018), 805–834
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