Lower $Q$-Homeomorphisms With Respect To $P$-Modulus And Orlicz-Sobolev Classes

TL;DR

This paper demonstrates that certain homeomorphisms with finite distortion in Orlicz-Sobolev classes are lower Q-homeomorphisms with respect to p-modulus, under Calderon-type conditions on the Orlicz function.

Contribution

It establishes the connection between finite distortion homeomorphisms in Orlicz-Sobolev spaces and lower Q-homeomorphisms with respect to p-modulus, extending previous results.

Findings

Homeomorphisms with finite distortion in $W^{1,}_{loc}$ are lower Q-homeomorphisms.

The function Q(x) equals the outer p-dilatation $K_{p,f}(x)$.

Results hold under Calderon-type conditions on $$.

Abstract

We show that under a condition of the Calderon type on $\varphi$ the homeomorphisms $f$ with finite distortion in $W^{1,\varphi}_{\rm loc}$ and, in particular, $f\in W^{1,s}_{\rm loc}$ for $s>n-1$ are the so-called lower $Q$-homeomorphisms with respect to $p$-modulus where $Q(x)$ is equal to its outer $p$-dilatation $K_{p,f}(x)$.