Differentiability of Mappings of the Sobolev Space Wn−11 with Conditions on the Distortion Function
- Authors: Vodopyanov S.K.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 59, No 6 (2018)
- Pages: 983-1005
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172089
- DOI: https://doi.org/10.1134/S0037446618060034
- ID: 172089
Cite item
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.
About the authors
S. K. Vodopyanov
Sobolev Institute of Mathematics
Author for correspondence.
Email: vodopis@math.nsc.ru
Russian Federation, Novosibirsk