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

Abstract

We give sharp conformal conditions for the differentiability in the Sobolev space W-loc(1,n-1) (Omega, R-n). Furthermore, we show that the space W-loc(1,n-1) (Omega, R-n) can be considered as the borderline space for some capacitary inequalities.

Keywords

• Mapping of finite distortion
• differentiability
• capacity