Asymptotic dilation of regular homeomorphisms
We study the asymptotic behavior of the ratio $|f(z)|/|z|$ as $z\to 0$ for homeomorphic mappings
differentiable almost everywhere in the unit disc with non-degenerated Jacobian. The main tools
involve the length-area functionals and angular dilatations depending on some real number $p.$
The results are applied to homeomorphic solutions of a nonlinear Beltrami equation. The estimates
are illustrated by examples.