Differentiability in the Sobolev space W1,n-1
Tengvall, V. (2014). Differentiability in the Sobolev space W1,n-1. Calculus of variations and partial differential equations, 51 (1-2), 381-399. doi:10.1007/s00526-013-0679-4
© Springer-Verlag Berlin Heidelberg 2013. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
Let Ω ⊂ Rn be a domain, n ≥ 2. We show that a continuous, open and discrete mapping f ∈ W1,n−1 loc (Ω, Rn ) with integrable inner distortion is differentiable almost everywhere on Ω. As a corollary we get that the branch set of such a mapping has measure zero.