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Differentiability of Mappings of the Sobolev Space Wn−11 with Conditions on the Distortion Function

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    S. K. Vodopyanov

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  1. S. K. Vodopyanov
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Correspondence to S. K. Vodopyanov.

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Original Russian Text © 2018 Vodopyanov S.K.

__________

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 6, pp. 1240–1267, November–December, 2018; DOI: 10.17377/smzh.2018.59.603.

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Vodopyanov, S.K. Differentiability of Mappings of the Sobolev Space Wn−11 with Conditions on the Distortion Function. Sib Math J 59, 983–1005 (2018). https://doi.org/10.1134/S0037446618060034

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  • DOI: https://doi.org/10.1134/S0037446618060034

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