Publication at Faculty of Mathematics and Physics |
2010
Abstract
The recent result shows that a homeomorphism $f\in W^{1,n-1}_{\loc}(\Omega,\rn)$ of finite distortion satisfies $f^{-1}\in W^{1,1}_{\loc}(f(\Omega),\rn)$. We show that this result is sharp in a sense that the crutial regularity condition $|Df|\in L^{n-1}$ cannot be replaced by $|\adj Df|\in L^1$ or by a requirement that $|Df|$ belongs to some bigger Orlicz space.