On the theory of hyper-$Q$-homeomorphisms

• Datum: 2010
• Hauptverfasser: Kovtonyuk, D. A., Ковтонюк, Д. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2010
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/2850
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We show that if a homeomorphism $f$ of a domain $D ⊂ R^n,\; n ≥ 2$, is a hyper-$Q$-homeomorphism with $Q ∈ L_{\text{loc}^1$ , then $f ∈ ACL$. As a consequence, this homeomorphism has partial derivatives and an approximation differential almost everywhere.