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) Charles University, Prague, Czech Republic
(2) University of 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