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

Abstract

We show that under a condition of the Calderon type on $\phi$ the homeomorphisms $f$ with finite distortion in $W_{\mathrm{loc}}^{1,\phi }$ and, in particular, $f\in W_{\mathrm{loc}}^{1,s}$ 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 $K_{p,f}(x)$.

arXiv admin note: text overlap with arXiv:1012.5010