On asymptotics of ring $Q$-homeomorphisms with respect to $p$-modulus near the origin

Abstract

We consider the class of ring $Q$-homeomorphisms with respect to $p$-modulus in $\mathbb{R}^{n}$ with $p > n$, and obtain lower bounds for limsups of the distance distortions under such mappings. These estimates can be treated as H\"{o}lder's continuity of the inverses near the origin. The sharpness is illustrated by example