# Revista Matemática Iberoamericana

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**Volume 33, Issue 2, 2017, pp. 595–622**

**DOI: 10.4171/RMI/951**

Sharpness of the differentiability almost everywhere and capacitary estimates for Sobolev mappings

Stanislav Hencl^{[1]}and Ville Tengvall

^{[2]}(1) Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00, Prague 8, Czechia

(2) Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014, Jyväskylä, Finland

We give sharp conformal conditions for the differentiability in the Sobolev space $W_{\mathrm {loc}}^{1,n-1}(\Omega, \mathbb R^{n})$. Furthermore, we show that the space $W_{\mathrm {loc}}^{1,n-1}(\Omega, \mathbb R^{n})$ can be considered as the borderline space for some capacitary inequalities.

*Keywords: *Mapping of finite distortion, differentiability, capacity

Hencl Stanislav, Tengvall Ville: Sharpness of the differentiability almost everywhere and capacitary estimates for Sobolev mappings. *Rev. Mat. Iberoamericana* 33 (2017), 595-622. doi: 10.4171/RMI/951