On ACL and hyper Q-homeomorphisms

D.A. Kovtoniuk

doi:10.15421/240713

On ACL and hyper Q-homeomorphisms

D.A. Kovtoniuk (Institute of Applied Mathematics and Mechanics of NAS of Ukraine)

Abstract

We show that, if homeomorphism $$$f$$$ of domain $$$D \subset \mathbb{R}^n$$$, $$$n \geqslant 2$$$, is a hyper Q-homeomorphism with $$$Q \in L_{loc}^1$$$, then $$$f \in ACL$$$. As a consequence, such homeomorphism has partial derivatives almost everywhere and approximative differential. Besides, it is possible to prove that external dilatation $$$K_O(x, f)$$$ of mapping $$$f$$$ is almost everywhere majorated by function $$$Q^{n-1}$$$ and $$$f \in W_{loc}^{1,1}$$$.

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