On the regularity of the Poletskii function under weak analytic assumptions on the given mapping (Q461892)

Given \(\Omega\subset\mathbb{R}^n\), a map \(f\in W^{1,n}_{\text{loc}}(\Omega,\mathbb{R}^n)\) is said to have finite distortion if \(|Df(x)|^n\leq k\text{\,det\,}Df(x)\) for all \(x\in\Omega\) and some constant \(k\geq 1\). In this paper, the author gives sufficient conditions on a continuous open discrete map \(f\in W^{1,q}_{\text{loc}}(\Omega, \mathbb{R}^n)\) \((q> n-1)\) under which \(f\) preserves orientation and the so-alled Poletskij index belongs to \(W^{1,1}\) and has finite distortion.