Mappings of \(L^p\)-integrable distortion: regularity of the inverse (Q2832282)

The authors study Sobolev homeomorphisms \(f: \mathbb{X}\to \mathbb{R}^n\) under \(L^p\)-integrability assumptions on the distortion function \(K_f\). If \( \mathbb{X}\) is the unit ball and \(p>n-1\), then the optimal modulus of continuity of \(f^{-1}\) is attained by a radially symmetric mapping.NEWLINENEWLINEAnswering a question raised by S. Hencl and P. Koskela, the authors then proceed to show that this is not the case when \(n\geq 3\) and \(p\leq n-1\).